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

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

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

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

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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]

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

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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

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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

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

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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

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

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

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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

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

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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

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

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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

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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

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

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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

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

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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

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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

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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

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

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

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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

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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 :

$=\frac{13}{6}$

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

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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

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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

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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

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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

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

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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

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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

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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

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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

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

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

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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

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

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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)

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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

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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

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

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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

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

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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.

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

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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.

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

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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

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

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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

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

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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)

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

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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

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

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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

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

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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

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

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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

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

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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

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

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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

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

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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

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

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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

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

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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

S.chand books class 8 maths solution chapter 4 Cube and Cube Roots exercise 4 B

EXERCISE 4 (B)

Number	Cube	Cube Root
1	1	1.000
2	8	1.260
3	27	1.442
4	64	1.587
5	125	1.710
6	216	1.817
7	343	1.913
8	512	2.000
9	729	2.080
10	1000	2.154
11	1331	2.224
12	1728	2.289
13	2197	2.351
14	2744	2.410
15	3375	2.466
16	4096	2.520
17	4913	2.571
18	5832	2.621
19	6859	2.668
20	8000	2.714
21	9261	2.759
22	10648	2.802
23	12167	2.844
24	13824	2.884
25	15625	2.924
26	17576	2.962
27	19683	3.000
28	21952	3.037
29	24389	3.072
30	27000	3.107
31	29791	3.141
32	32768	3.175
33	35937	3.208
34	39304	3.240
35	42875	3.271
36	46656	3.302
37	50653	3.332
38	54872	3.362
39	59319	3.391
40	64000	3.420
41	68921	3.448
42	74088	3.476
43	79507	3.503
44	85184	3.530
45	91125	3.557
46	97336	3.583
47	103823	3.609
48	110592	3.634
49	117649	3.659
50	125000	3.684
51	132651	3.708
52	140608	3.733
53	148877	3.756
54	157464	3.780
55	166375	3.803
56	175616	3.826
57	185193	3.849
58	195112	3.871
59	205379	3.893
60	216000	3.915
61	226981	3.936
62	238328	3.958
63	250047	3.979
64	262144	4.000
65	274625	4.021
66	287496	4.041
67	300763	4.062
68	314432	4.082
69	328509	4.102
70	343000	4.121
71	357911	4.141
72	373248	4.160
73	389017	4.179
74	405224	4.198
75	421875	4.217
76	438976	4.236
77	456533	4.254
78	474552	4.273
79	493039	4.291
80	512000	4.309
81	531441	4.327
82	551368	4.344
83	571787	4.362
84	592704	4.380
85	614125	4.397
86	636056	4.414
87	658503	4.431
88	681472	4.448
89	704969	4.465
90	729000	4.481
91	753571	4.498
92	778688	4.514
93	804357	4.531
94	830584	4.547
95	857375	4.563
96	884736	4.579
97	912673	4.595
98	941192	4.610
99	970299	4.626
100	1000000	4.642

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Q1 | Ex-4B | Class 8 | Cube and Cube roots | S.Chand | Composite Mathematics | myhelper

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Question 1

Find the cube roots of the following numbers using table.

(i) 28

(ii) 61

(iii) 83

(iv) 350

(v) 570

(vi) 960

(vii) 4.3

(viii) 6600

(ix) 9.4

(x) 6.9

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Q2 | Ex-4B | Class 8 | Cube and Cube roots | S.Chand | Composite Mathematics | myhelper

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Question 2

Find the cube roots of

(i) 76.25

(ii) 37.62

(iii) 458

(iv) 732