Showing posts with label Squares and Square roots. Show all posts
Showing posts with label Squares and Square roots. Show all posts

S.chand Class 8 Maths Solution Chapter 3 Squares and Square roots Exercise 3C

 Exercise 3C

Q1 | Ex-3C | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 1

Find the square root of each of the following numbers correct to two places of decimal :

(i) 3

(ii) 23

(iii) 478

(iv) 789


Q2 | Ex-3C | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 2

Find the square root of each of the following decimal numbers correct to 2 places of decimal :

(i) 175.01

(ii) 423.74

(iii) 5893.27

(iv) 7136.8


Q3 | Ex-3C | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 3

Find the square root of each of the following fractional numbers correct to 2 places of decimal :

(i) $\frac{4}{7}$

(ii) $\frac{13}{11}$

(iii) $1 \frac{7}{8}$

(iv) $83 \frac{7}{11}$






















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S.chand Class 8 Maths Solution Chapter 3 Squares and Square roots Exercise 3B

 Exercise 3B

Q1 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 1

Find by prime factorization the square root of the following numbers :

(i) 2916

(ii) 2704

(iii) 7056

(iv) 9025

(v) 9216

Sol :






Q2 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 2

Find the square root of the following fractions :

(i) $\frac{25}{49}$

(ii) $\frac{196}{484}$

(iii) $\frac{1225}{2025}$

(iv) $0.0009$

(v) $0.00000049$

Sol :






Q3 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 3

Simplify :

(i) $\sqrt{\left(5^{2}-4^{2}\right)}$

(ii) $\sqrt{\left(5^{2}+12^{2}\right)}$

(iii) $\left(\frac{1}{2}\right)^{2}+\sqrt{0.25}$

(iv) $\left(-\sqrt{\frac{4}{9}}\right)\left(-\sqrt{\frac{81}{100}}\right)$

Sol :






Q4 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 4

Find the square root of each of the following numbers by long division :

(i) 6724

(ii) 7921

(iii) 8649

(iv) 9801

(v) 15129

Sol :






Q5 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 5 

Find the square root of each of the following decimal numbers by long division :

(i) $4556.25$

(ii) $6099.61$

(iii) $7903.21$

(iv) $9273.69$

Sol :






Q6 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 6

Evaluate :

(i) $\sqrt{\frac{2809}{4096}}$

(ii) $\sqrt{\frac{1849}{5776}}$

(iii) $\sqrt{1 \frac{869}{1156}}$

Sol :








Q7 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 7

Find the value of $\sqrt{9216}$ and from this value calculate $\sqrt{92.16}+9.216$.

Sol :








Q8 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 8

Find the square roots of 2116 and 1764 and hence find the value of $\frac{\sqrt{0.2116}+\sqrt{0.1764}}{\sqrt{0.2116}-\sqrt{0.1764}}$.

Sol :






Multiple Choice Questions (MCQs)

Q9 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 9

The value of $\frac{3}{\sqrt{0.09}}$ is :

(a) $\frac{1}{10}$

(b) $\frac{3}{10}$

(c) 1

(d) 10

Sol :








Q10 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 10

Of the numbers $0.16, \sqrt{0.16},(0.16)^{2}$ and $0.016$ the least number is

(a) $(0.16)^{2}$

(b) $\sqrt{0.16}$

(c) $0.016$

(d) $0.16$

Sol :






Q11 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 11

$\sqrt{0.0025} \times \sqrt{2.25} \times \sqrt{0.0001}$ equals

(a) $0.000075$

(b) $0.0075$

(c) $0.075$

(d) $0.00075$

Sol :






Q12 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 12

The square root of $\sqrt{2 \frac{1337}{3844}}$ is

(a) $2 \frac{35}{64}$

(b) $1 \frac{33}{62}$

(c) $1 \frac{17}{62}$

(d) $2 \frac{23}{62}$

Sol :







Q13 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 13

$\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}$ equals

(a) 1

(b) 0.65

(c) 0.45

(d) 0.54

Sol :







Q14 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 14

3600 soldiers are asked to stand in different rows. Every row has as many soldiers as there are rows. Find the number of rows.

Sol :







Q15 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 15

Find the perimeter of a square whose area is $6889 \mathrm{~m}^{2}$.

Sol :








Q16 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 16

A society collected ₹ 8836, each member contributing as many rupees as there were members. Find the number of members of the society.

Sol :








Q17 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 17

In a basket there are 1250 flowers. A man goes for worship and puts as many flowers as there are temples in the city. Thus he needs 8 baskets of flowers. Find the number of temples in the city.

Sol :







Q18 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 18

What should be subtracted from 6249 to get a perfect square number? What is this perfect square number? Also, find its square root.

Sol :







Q19 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 19

What least number must be added to 594 to make the sum a perfect square ?

Sol :







Q20 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 20

What would be added to 7912 to make the sum a perfect square ?

Sol :







Q21 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 21

Find the least number of six digits which is a perfect square.

Sol :








Q22 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 22

A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8341 , find the number of soldiers in each row.

Sol :







High Order Thinking Skills (HOTS)

Q23 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 23

Find $: \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}$

Sol :







Q24 | Ex-3B | Class 8 | SChand Composite maths | Squares and Square roots | Chapter 3 | myhelper

Question 24

Find the value of $\sqrt{1191.16+70 \sqrt{129.96}}$.

Sol :






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S.chand Class 8 Maths Solution Chapter 3 Squares and Square roots Exercise 3A

 Exercise 3A

Q1 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 1

Using the prime factorization method, find which of the following numbers are not perfect squares:

(i) 400

(ii) 768

(iii) 1296

(iv) 8000

(v) 9025




Q2 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 2

Find the smallest number by which each of the given numbers must be multiplied so that the product is a perfect square :

(i) 512

(ii) 700

(iii) 1323

(iv) 35280




Q3 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 3

Find the smallest number by which each of the given numbers should be divided so that the result is a perfect square :

(i) 180

(ii) 1575

(iii) 6912

(iv) 19200



Q4 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 4

Answer True (T) or False (F) :

(i) The number of digits in a square number are always even.

(ii) The square of a prime number is prime.

(iii) No square number is negative.

(iv) The difference of two square numbers is a square number.

(v) 4000 is a square number.



Q5 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 5

Just by looking at the following numbers, give reasons why they are not perfect squares.

(i) 2367

(ii) 57000

(iii) 35943

(iv) 4368

(v) 333222



Q6 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 6

What will be the units digit of the squares of the following numbers ?

(i) 539

(ii) 731

(iii) 8593

(iv) 23904

(v) 39487

(vi) 39065

(vii) 7358

(viii) 5980



Q7 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 7

Fill in the blanks : (Use a property of square numbers)

(i) $19^{2}-18^{2}$=___

(ii) $30^{2}-29^{2}$=___

(iii) $87^{2}-86^{2}$=___



Q8 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 8

Without adding, match the sum in Column A with the perfect square in Column B.

Column AColumn B
(i) 1+3+5+7+9
(ii) 1+3+5+7+9+11+13+15
(iii) 1+3+5
(iv) 1+3+5+7+9+11
(v) 1+3+5+7+9+11+13+15+17+19		(a) 36
(b) 100
(c) 25
(d) 64
(e) 9



Q9 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 9

Which of the following triplets are Pythagorean ?

(i) (10,24,26)

(ii) (14,48,50)

(iii) (18,79,82)

(iv) (22,120,122)


Multiple Choice Questions (MCQs)


Q10 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 10

10. Which number is NOT a perfect square ?

(a) 64

(b) 169

(c) 288

(d) 400



Q11 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 11

The smallest number by which 980 must be multiplied so that the product is a perfect square is

(a) 7

(b) 5

(c) 3

(d) 6



Q12 |Ex-3A | Squares and Square roots |Class 8 |Schand composite maths | myhelper

Question 12

For every natural number ' n ', $(n+1)^{2}-n^{2}$ equals.

(a) n-(n+1)

(b) (n+1)-n

(c) (n-1)+n

(d) (n+1)+n


















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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3E

 Exercise 3E

Q1 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 1

Find the cubes of the following numbers.

(a) 123

Sol : 1728


(b) 153

Sol : 3375


(c) 503

Sol : 125000


(d) 2003

Sol : 8000000


(e) $\left(-\frac{3}{7}\right)^3$

Sol : $-\frac{27}{343}$


(f) $1\frac{3}{8}^3$

Sol : $\frac{11}{8}^3=\frac{1331}{512}$


(g) 0.43

Sol : $=\frac{4}{10}=\frac{64}{1000}$

=0.064


(h) 0.93

Sol : $=\frac{9}{10}^3=\frac{729}{1000}$

=0.729


(i) 0.023

Sol : $=\frac{2}{100}^3=\frac{8}{1000000}$

=0.000008


(j) $-2\frac{2}{9}^3$

Sol : $-\frac{20^3}{9}=-\frac{8000}{729}$


Q2 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 2

Which of the following numbers are perfect cubes?

(a) 125

Sol : 5×5×5

[perfect cube]


(b) 2197

Sol : 13×13×13

[perfect cube]


(c) 832

Sol : 2×2×2×2×2×2×13

[not a perfect cube]


(d) 2744

Sol : 2×2×2×7×7×7

[perfect cube]


(e) 2000

Sol : 5×5×5×4×4

[not a perfect cube]


Q3 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 3

What is the smallest natural number by which the following should be multiplied so that they become perfect cubes?

(a) 36

Sol : 2×2×3×3

=2×3=6 need smallest natural number 6 for perfect cube


(b) 121

Sol : 11×11=11  need smallest natural number 11 for perfect cube


(c) 392

Sol : 2×2×2×7×7=7 need smallest natural number 7 for perfect cube


Q4 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 4

What is the smallest natural number by which the following numbers should be divided so that they become perfect cubes?

(a) 54

Sol : 2×3×3×3

divided by 2


(b) 625

Sol : 5×5×5×5

divided by 5


(c) 1536

Sol : 2×2×2×2×2×2×2×2×2×3

divided by 3


(d) 7000

Sol : 7×5×5×5×2×2×2

divided by 7


Q5 |Ex-3E |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 5

Find the cube root of each of the following numbers by prime factorisation method.

(a) 8

Sol : 2×2×2=2


(b) 216

Sol : 6×6×6=6


(c) 1728

Sol : 2×2×2×3×3×3=12


(d) $-4\frac{17}{27}$

Sol : $=-\frac{125}{27}=-\frac{5\times 5\times 5}{3\times 3\times 3}$


(e) 0.027

Sol : $=\frac{27}{1000}=\frac{3\times 3\times 3}{10\times 10\times 10}=\frac{3}{10}$

=0.3


(f) -.216

Sol : $=\frac{216}{1000}=\frac{6\times 6\times 6}{10\times 10\times 10}=\frac{6}{10}$

=06


(g) 0.001331

Sol : $=\frac{1331}{1000000}=\frac{11\times 11\times 11}{100\times 100\times 100}=\frac{11}{100}$

=0.11


(h) 0.002744

Sol : $=\frac{2744}{1000000}=\frac{14\times 14\times 14}{100\times 100\times 100}=\frac{14}{100}$

=0.14

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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3D

 Exercise 3D

Q1 |Ex-3D |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 1

Find the least number which must be subtracted from each of the following numbers to make it perfect square.

(a) 740

Sol :

$\begin{array}{r|l}&27\\ \hline 2&740\\&4\\\hline 47&340 \\ &329\\ \hline &11\\\end{array}$

∴Remainder=11

∴Now subtract 11 from 740. Then we get a perfect square.

∴740-11=729

∴√729=27


(b) 1535

Sol :

$\begin{array}{r|l}&39\\ \hline 3&1535\\&9\\\hline 69&635 \\ &621\\ \hline &14\\\end{array}$

∴Remainder=14

∴Now subtract 14 from 1535. Then we get a perfect square.

∴1535-14=1521


(c) 7926

Sol :

$\begin{array}{r|l}&89\\ \hline 8&7926\\&64\\\hline 169&1526 \\ &1521\\ \hline &5\\\end{array}$

∴Remainder=5

∴Perfect square=7926-5=7921


Q2 |Ex-3D |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 2

Find the least number which must be added to each of the following numbers to make it a perfect square.

(a) 708

Sol :
$\begin{array}{r|l}&26\\ \hline 2&708\\&4\\\hline 46&308 \\ &276\\ \hline &32\\\end{array}$

∴We observe that

262<708<272


∴The number to be added

=272-708

=729-708

=21

Then, 708 would become=708+21=729
∴√729=27


(b) 1840

Sol :

$\begin{array}{r|l}&42\\ \hline 4&1840\\&16\\\hline 82&240 \\ &164\\ \hline &76\\\end{array}$

∴We observe that

422<1840<432


∴The number to be added

=432-1840

=1849-1840

=9


(c) 3219

Sol :

$\begin{array}{r|l}&56\\ \hline 5&3219\\&25\\\hline 106&719 \\ &636\\ \hline &83\\\end{array}$

∴We observe that

562<3219<572


∴The number to be added

=572-3219

=3249-3219

=30


Q3 |Ex-3D |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 3

4225 soldiers are arranged in different rows so that there are as many rows as the number of soldiers in a row. Find the number of rows.

Sol :

The number of rows=4225

=√4225=65


Q4 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 4

A gardener plants 3364 trees in such a way that there are as many rows as there are trees in a row. Find the number of trees in a row.

Sol :

The number of trees in a row=√3364

=58


Q5 |Ex-3D |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 5

A club collected Rs. 7225 for a charity. Each member contributed as many rupees as there were number of members of the club. How many members does the club have.

Sol :

Members of the club=√7225

=85

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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3C

 Exercise 3C

Q1 | Ex-3C | Class 8 | Squares and Square roots,Cube and Cube roots | New Learning Composite maths | Schand Solution | myhelper


Question 1

Find the square root of each of the following numbers by long division method.

(a) 484

Sol :

$\begin{array}{r|l}&22\\\hline 2&484\\&4\\\hline 42&84\\ &84\\ \hline &\times\end{array}$


(b) 841

Sol :

$\begin{array}{r|l}&29\\\hline 2&841\\&4\\\hline 49&441\\ &441\\ \hline &\times\end{array}$


(c) 1849

Sol :

$\begin{array}{r|l}&43\\\hline 4&1849\\&16\\\hline 83&249\\ &249\\ \hline &\times\end{array}$


(d) 2704

Sol :

$\begin{array}{r|l}&52\\\hline 5&2704\\&25\\\hline 102&204\\ &204\\ \hline &\times\end{array}$


(e) 4624

Sol :

$\begin{array}{r|l}&68\\\hline 6&4624\\&36\\\hline 128&1024\\ &1024\\ \hline &\times\end{array}$


(f) 6724

Sol :

$\begin{array}{r|l}&82\\\hline 8&6721\\&64\\\hline 162&321\\ &321\\ \hline &\times\end{array}$


(g) 7569

Sol :

$\begin{array}{r|l}&87\\\hline 8&7569\\&64\\\hline 167&1169\\ &1169\\ \hline &\times\end{array}$


(h) 9801

Sol :

$\begin{array}{r|l}&99\\\hline 9&7801\\&81\\\hline 189&1701\\ &1701\\ \hline &\times\end{array}$


Q2 | Ex-3C | Class 8 | Squares and Square roots,Cube and Cube roots | New Learning Composite maths Schand Solution | myhelper

Question 2

(a) $7\frac{522}{529}$

Sol :

⇒$\frac{4225}{529}$

$\begin{array}{r|l}&23\\\hline 2&529\\&4\\\hline 43&129\\ &129\\ \hline &\times\end{array}$

$\begin{array}{r|l}&65\\\hline 6&4225\\&36\\\hline 125&625\\ &625\\ \hline &\times\end{array}$

∴$\frac{4225}{529}=\frac{65}{23}=2 \frac{19}{23}$


(b) $8\frac{617}{784}$

Sol :

⇒$\frac{6889}{784}$

$\begin{array}{r|l}&83\\\hline 8&6889\\&64\\\hline 163&489\\ &489\\ \hline &\times\end{array}$

$\begin{array}{r|l}&28\\\hline 2&784\\&4\\\hline 48&384\\ &384\\ \hline &\times\end{array}$

∴$\frac{6889}{784}=\frac{83}{28}=2 \frac{27}{28}$


(c) $2\frac{766}{2209}$

Sol :

⇒$\frac{5184}{2209}$

$\begin{array}{r|l}&72\\\hline 7&5184\\&49\\\hline 142&284\\ &284\\ \hline &\times\end{array}$

$\begin{array}{r|l}&47\\\hline 4&2209\\&16\\\hline 87&609\\ &609\\ \hline &\times\end{array}$

∴$\frac{5184}{2209}=\frac{72}{47}=1 \frac{25}{47}$


Q3 | Ex-3C | Class 8 | Squares and Square roots,Cube and Cube roots | New Learning Composite maths Schand Solution | myhelper

Question 3

(a) 3.24

Sol :

⇒$\frac{324}{100}$

$\begin{array}{r|l}&10\\\hline 1&100\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&18\\\hline 1&324\\&1\\\hline 28&224\\ &224\\ \hline &\times\end{array}$

∴$\frac{324}{10}=\frac{18}{10}$=1.8


(b) 6.25

Sol :

⇒$\frac{625}{100}$

$\begin{array}{r|l}&10\\\hline 1&100\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&25\\\hline 2&625\\&4\\\hline 45&225\\ &225\\ \hline &\times\end{array}$

∴$\frac{625}{100}=\frac{25}{10}$=2.5


(c) 11.56

Sol :

⇒$\frac{1156}{100}$

$\begin{array}{r|l}&10\\\hline 1&100\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&34\\\hline 3&1156\\&9\\\hline 64&256\\ &256\\ \hline &\times\end{array}$

∴$\frac{1156}{100}=\frac{34}{10}$=3.4


(d) 16.81

Sol :

⇒$\frac{1681}{100}$

$\begin{array}{r|l}&10\\\hline 1&100\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&41\\\hline 4&1681\\&16\\\hline 81&81\\ &81\\ \hline &\times\end{array}$

∴$\frac{1681}{100}=\frac{41}{10}$=4.1


(e) 22.09

Sol :

⇒$\frac{2209}{100}$

$\begin{array}{r|l}&10\\\hline 1&100\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&47\\\hline 4&2209\\&16\\\hline 87&609\\ &609\\ \hline &\times\end{array}$

∴$\frac{2209}{100}=\frac{47}{10}$=4.7


(f) 0.5041

Sol :

⇒$\frac{5041}{1000}$

$\begin{array}{r|l}&100\\\hline 1&10000\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&71\\\hline 7&5041\\&49\\\hline 141&141\\ &141\\ \hline &\times\end{array}$

∴$\frac{5041}{10000}=\frac{71}{100}$=0.71


(g) 0.5625

Sol :

⇒$\frac{5625}{1000}$

$\begin{array}{r|l}&100\\\hline 1&10000\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&75\\\hline 7&5625\\&49\\\hline 145&725\\ &725\\ \hline &\times\end{array}$

∴$\frac{5625}{10000}=\frac{75}{100}$=0.75


(h) 0.9216

Sol :

⇒$\frac{9216}{1000}$

$\begin{array}{r|l}&100\\\hline 1&10000\\&1\\\hline &\times\end{array}$

$\begin{array}{r|l}&46\\\hline 9&9216\\&81\\\hline 186&1116\\ &1116\\ \hline &\times\end{array}$

∴$\frac{9216}{10000}=\frac{96}{100}$=0.96

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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3B

 Exercise 3B

Q1 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 1

Find the two square roots of the following numbers.

(a) 4

Sol : 2,-2


(b) 81

Sol : 9,-9


(c) 196

Sol : 14,-14


(d) 400

Sol : 20,-20


(e) 441

Sol : 21,-21


(f) 0.0049

Sol : 0.07, -0.07


(g) 0.0001

Sol : 0.01, -0.01


(h) $3\frac{1}{16}$

Sol : $\frac{7}{4},-\frac{7}{4}$


(i) $2\frac{1}{4}$

Sol : $\frac{3}{2},-\frac{3}{2}$


(j) 0.0289

Sol : 0.17 , -0.17


Q2 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 2

Evaluate the following.

(a) √36

Sol :

=2×2×3×3

=2×3

=6


(b) -√9

Sol : =-(3×3)

=-3


(c) √121

Sol : =11×11×11


(d) -√225

Sol :

=-(5×5×3×3)

=-(5×3)

=-15


(e) √361

Sol :

=19×19

=19


(f) √900

Sol :

=30×30

=30


(g) √0.09

Sol :

=0.3×0.3=0.3


(h) √0.0256

Sol :

=0.16×0.16

=0.16


(i) √2.25

Sol :

=1.5×1.5

=1.5


(j) $\sqrt{4\frac{25}{36}}$

Sol :

$=\frac{13}{6}$


Q3 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 3

Solve

(a) x2 = 1

Sol : x=±1


(b) 12x2 = 108

Sol :

$x^2=\frac{108}{2}=9$

x=±3


(c) x2 – 17 = -1

Sol :

x2=-(16)

x=±4


(d) x2=$\frac{16}{25}$

Sol :

x2=$\pm \frac{4}{5}$


Q4 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 4

Find the square root of each of the following numbers by the prime factorisation method.

(a) 484

Sol :

=2×2×11×11

=2×11=22


(b) 2500

Sol :

=2×2×5×5×5×5

=2×5×5

=50


(c) 2025

Sol :

=5×5×9×9

=5×9

=45


(d) 2916

Sol :

=2×2×3×3×9×9

=2×3×9=54


(e) 2401

Sol :

=7×7×7×7

=7×7=49


(f) 6084

Sol :

=2×2×3×3×13×13

=2×3×13=78


(g) $1\frac{184}{441}$

Sol :

$=\frac{625}{441}=\frac{25\times 25}{21\times 21}$

$=\frac{25}{21}$


(h) 0.1936

Sol :

$=\frac{1936}{10000}=\frac{44\times 44}{10\times 10\times 10 \times 10}$

$=\frac{44}{100}$=0.44


(i) 0.0576

Sol :

$=\frac{576}{10000}=\frac{24\times 24}{10\times 10\times 10\times 10}$

$=\frac{24}{100}$=0.24


(j) 40.96

Sol :

$=\frac{4096}{100}=\frac{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times }{10\times 10}$

$=\frac{64}{100}$=0.64


Q5 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite

Question 5

Find the smallest whole number for each of the following numbers by which it should be multiplied so as to get a perfect square number.

(a) 768

Sol :

=2×2×2×2×2×2×2×2×3

∴Multiplied by 3


(b) 200

Sol :

=5×5×2×2×2

∴Multiplied by 2


(c) 2880

Sol :

=2×2×2×2×2×2×3×3×5

∴Multiplied by 5


(d) 16807

Sol :

=7×7×7×7×7

∴Multiplied by 7


(e) 1331

Sol :

=11×11×11

∴Multiplied by 11


Q6 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 6

Find the smallest whole number for each of the following numbers by which it should be divided so as to get a perfect square number.

(a) 3125

Sol :

=5×5×5×5×5

∴Divided by 5


(b) 1800

Sol :

=2×2×2×5×5×3×3

∴Divided by 2


(c) 1008

Sol :

=2×2×2×2×3×3×7

∴Divided by 7


(d) 6912

Sol :

=2×2×2×2×2×2×2×2×3×3×3

∴Divided by 3


(e) 2925

Sol :

=13×15×15

∴Divided by 13


Q7 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 7

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

Sol :

⇒8,15 & 20

⇒L.C.M of 8,15,20 is 120

∴Prime factor of 120=2×2×[2×3×5]

=30

∴The factor 30 remains unpaired so to make 120 a perfect square it should be multiplied by 30

∴The smallest square number=120×30

=3600


Q8 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 8

Find the least square number, which is exactly divisible by 3, 4, 5, 6 and 8.

Sol :

L.C.M of 3,4,5,6,8=120

∴Prime factor of 120=2×2×[2×3×5]

=30

∴Least square number=120×30

=3600


Q9 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 9

The area of a square plot is $101 \frac{1}{400}$ meter square, Find the length of one side of the plot.

Sol :

ATQ

$a^2=101\frac{1}{400}$ m2

∴$a=\sqrt{101\frac{1}{400}}=\sqrt{\frac{40401}{400}}$

∴$a=\pm \frac{201}{20}=10\frac{1}{20}$

∴One side of plot$=10\frac{1}{20}$ m


Q10 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 10

Find the value of $=\sqrt{162+\sqrt{38 + \sqrt{121}}}$

Sol :

$=\sqrt{162+\sqrt{38+11}}$

$=\sqrt{162+\sqrt{49}}=\sqrt{162+7}$

=√169=13


Q11 |Ex-3B |Class 8 |Squares and Square roots,Cube ,Cube roots |S.Chand New Learning Composite


Question 11

Given that √3136 = 56, find the value of √31.36 + √0.3136

Sol :

=√31.36 + √0.3136

$=\sqrt{\frac{3136}{100}}+\sqrt{\frac{3136}{10000}}$

$=\frac{56}{10}+\frac{56}{10}$

$=\frac{560+560}{1000}$

$=\frac{616}{100}$=6.16

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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 3 Squares and Square roots,Cube and Cube roots Exercise 3A

 Exercise 3A

Q1 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper


Question 1

Find the following squares:

(a) 122

Sol :

=12×12=144

(b) 92

Sol :

=9×9=81


(c) 282

Sol :

=28×28=784


(d) 392

Sol :

=39×39=1521


(e) 2152

Sol :

=215×215=46,225


Q2 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 2

Factories and find the which of the following numbers are not perfect squares.

(a) 784

Sol :

=2×2×2×2×7×7 (perfect square)


(b) 1296

Sol :

=2×2×2×2×9×9 (perfect square)


(c) 7500

Sol :

=5×5×5×5×5×5×3 (not perfect square)


(d) 5184

Sol :

=2×2×2×2×2×2×9×9 (perfect square)


(e) 980

Sol :

=2×2×7×7×5 (not perfect square)


(f) 4050

Sol :

=2×5×5×9×9 (not perfect square)


Q3 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 3

Find the smallest number by which each of the given numbers must be multiplied so that the product is a perfect square.

(a) 240

Sol :

=2×2×2×2×[3×5]

∴multiplied by 15


(b) 432

Sol :

=2×2×2×2×3×3×[3]

∴multiplied by 3


(c) 2592

Sol :

=2×2×2×2×[2]×9×9

∴multiplied by 2


(d) 18000

Sol :

=2×2×2×2×3×3×5×5×[5]

∴multiplied by 5


(e) 21952

Sol :

=2×2×2×2×2×2×7×7×[7]

∴multiplied by 7


Q4 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 4

Find the smallest number by which each of the following numbers should be divided so that question may be perfect square.

(a) 98

Sol :

=[2]×7×7

∴divided by 2


(b) 363

Sol :

=[3]×11×11

∴divided by 3


(c) 700

Sol :

=[7]×2×2×5×5

∴divided by 7


(d) 4400

Sol :

=[11]×2×2×2×2×5×5

∴divided by 11


(e) 4374

Sol :

=[2×3]×3×3×9×9

∴divided by 6


Q5 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 5

Just by looking at the following numbers, decide which of them

(i) may or may not be perfect squares

(ii) cannot be perfect squares. Give reasons.

[Note: If Unit digit is 2,3,7,8 or number of zeros is odd then its not a perfect square]


(a) 537

Sol :

=3×179 (not perfect square)

Reasons: pairs not found


(b) 1042

Sol :

=2×521 (not perfect square)

Reasons: pairs not found


(c) 800

Sol :

=2×2×2×2×[2]×5×5 (not perfect square)

Reasons: pairs not found


(d) 384

Sol :

=2×2×2×2×2×2×[2×3] (not perfect square)

Reasons: pairs not found


(e) 625

Sol :

=25×25 (perfect square)

Reasons: pair is found


(f) 6398

Sol :

=2×7×457 (not perfect square)

Reasons: pair not found


(g) 33493

Sol :

=3 is unit digit (not perfect square)

Reasons: pair not found


(h) 960

Sol :

=2×2×2×2×2×2×[3×5] (not perfect square)

Reasons: pair not found


(i) 72000

Sol :

=2×2×2×2×2×2×3×3×5×5×[5] (not perfect square)

Reasons: pair not found (Number of zeros are odd)


(j) 1571

Sol :

1571 is a prime number.(not perfect square)

Reasons: pair not found


Q6 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 6

Which of the following numbers would end with digit 1?

(a) 6092

(b) 3272

(c) 3252

(d) 3412

(e) 5462

Sol :

There is no need to find square of whole number , just find square of their unit digit .

(a) 92=81 and (d) 12=1

So, as you can see (a) and (d) end with unit digit 1.


Q7 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 7

Which of the following numbers would have digit 6 at units place?

(a) 732

(b) 3242

(c) 2762

(d) 7322

(e) 2942

Sol :

There is no need to find square of whole number , just find square of their unit digit .

here,(b) 42=16 , (c) 62=36 and (e) 42=16

So,(b),(c) and (e) end with unit digit 6.


Q8 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 8

What will be the units digit in the squares of the following numbers?

(a) 642

Sol : =42=16 

unit digit=6


(b) 932

Sol : =32=9

unit digit=9


(c) 2062

Sol : =62=36 

unit digit=6


(d) 1352

Sol : =52=25 

unit digit=5


(e) 4992

Sol : =92=81 

unit digit=1


(f) 2382

Sol :

Sol : =82=64 

unit digit=4


(g) 6072

Sol : =72=49 

unit digit=9


(h) 6522

Sol : =22=4 

unit digit=4


(i) 6502

Sol : =02=0 

unit digit=0


(j) 9712

Sol :

Sol : =12=1 

unit digit=1


Q9 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 9

The square of which of the following numbers would be an odd number/ even number? Why?

(a) 517

Sol :  267289➝odd


(b) 234

Sol :  54756➝even


(c) 300

Sol :  90000➝even


(d) 718

Sol :  515524➝even


(e) 945

Sol :  893025➝odd


(f) 719

Sol :  516961➝odd


Q10 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 10

What will be the following number of zeros in the square of the numbers?

(a) 40

Sol :  1600 

Number of zeros=(2)


(b) 400

Sol :  160000

Number of zeros=(4)


(c) 8000

Sol :  64000000

Number of zeros=(6)


(d) 60,000

Sol :  3600000000 

Number of zeros=(8)


Q11 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 11

How many natural numbers lie between

(a) 62 and 72

Sol : 6×2=12


(b) 192 and 202

Sol : 19×2=38


(c) 492 and 502

Sol : 49×2=98


(d) 752 and 762

Sol : 75×2=150


Q12 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 12

How many non-square numbers lie between the following pairs of numbers?

(i) 1002 and 1012

Sol : 100×2=200


(ii) 2152 and 2162

Sol : 215×2=430


(iii) 5002 and 5012

Sol : 500×2=1000


Q13 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 13

Express the following as the sum of two consecutive natural numbers.

(i) 232

Sol : $=\frac{23^2-1}{2}+\frac{23^2+1}{2}$

=264+265


(ii) 152

Sol : $=\frac{15^2-1}{2}+\frac{15^2+1}{2}$

=112+113


(iii) 192

Sol : $=\frac{19^2-1}{2}+\frac{19^2+1}{2}$

=180+181


(iv) 252

Sol : $=\frac{25^2-1}{2}+\frac{25^2+1}{2}$

=321+313


(v) 172

Sol : $=\frac{17^2-1}{2}+\frac{17^2+1}{2}$

=144+145


Q14 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 14

Using property of square numbers, find

(i) 242 – 232

Sol : 47


(ii) 592 – 582

Sol : 117


(iii) 752 – 742

Sol : 149


(iv) 1022 – 1012

Sol : 203


Q15 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 15

Using adding, find the sum of the following sets of odd numbers.

(a) 1 + 3 + 5 + 7 + 9

Sol : 52=25


(b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Sol : 102=100


(c) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Sol : 122=144


Q16 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 16

Express:

(a) 169 as the sum of 13 odd numbers.

Sol :

=1+3+5+7+9+11+13+15+17+19+21+23+25


(b) 64 as the sum of 8 odd numbers.

Sol :

=1+3+5+7+9+11+13+15


Q17 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 17

Which of the following sets of three numbers form a Pythagorean triples?

(a) (6, 8, 10)

Sol :

2m⇒$m=\frac{6}{2}$=3

m2-1=32-1=4-1=8

m2+1=32+1=9+1=10

∴ 6,8 and 10 is in Pythagorean triples


(b) (14, 18, 50)

Sol :

2m⇒$m=\frac{14}{2}$=7

m2-1=72-1=49-1=48

m2+1=72+1=49+1=50

∴ It is not Pythagorean triples


(c) (7, 9 ,12)

Sol :

2m⇒$m=\frac{7}{2}$

m2-1

m2+1

∴ It is not Pythagorean triples


(d) (16, 63, 65)

Sol :

2m⇒$m=\frac{16}{2}$=8

m2-1=82-1=64-1=63

m2+1=82+1=64+1=65

∴ It is in Pythagorean triples


(e) (12 ,25 ,37)

Sol :

2m⇒$m=\frac{12}{2}$=6

m2-1=62-1=36-1=35

m2+1=62+1=36+1=37

∴ It is not Pythagorean triples


Q18 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 18

Observe the following pattern and supply the missing digits

112 = 121

1012 = 10201

10012 = 1002001

100012 = 100020001

1000012 = 1___2___1

100000012 =  1___2___1

Sol :

112=121

1012=10201

10012=1002001

100012=100020001

1000012=10000200001

100000012=100000020000001


Q19 | Ex-3A |Class 8 |Exponents | S.Chand | New Learning |Composite maths |Chapter 3 | myhelper

Question 19

Using the given pattern find the missing number

12 + 22 + 22 = 32

22 + 32 + 62 = 72

32 + 42 + 122 = 132

42 + 52 + ____2 = 212

52 + ____2 + 302 = 312

62 + 72 + ______2 = _____2

Sol :

12 + 22 + 32 = 32

22 + 32 + 62 = 72

32 + 42 + 122 = 132

42+52+202=212

52+62+302=312

62+72+422=432

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