S.chand Composite Mathematics class 8 Chapter 3 Square and Square Roots Exercise 3B

Exercise 3 (B)

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Q1 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 1

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

(i) 3249

Sol :

$\begin{array}{r|l}  &57 \\\hline5&3249\\5&25\\\hline 107 & ~~749 \\ 7&~~749\\\hline &~~~~0 \end{array}$

(ii) 6889

Sol :

$\begin{array}{r|l} &83 \\\hline 8&6889\\8&64\\\hline 163 & ~~489 \\ 3&~~489\\\hline &~~~~0 \end{array}$

(iii) 15129

Sol :

$\begin{array}{r|l} &123 \\\hline 1&15129\\1&1\\\hline 22 & ~~51 \\ 2&~~44\\\hline 243&~~~~~~729\\&~~~~~~729\\ \hline &~~~~~~~~0 \end{array}$

(iv) 75625

Sol :

$\begin{array}{r|l} &275 \\\hline 2&75625\\2&4\\\hline 47 & 356 \\7&329\\\hline 545&~~2725\\5&~~2725\\ \hline &~~~~~0 \end{array}$

(v) 166464

Sol :

$\begin{array}{r|l} &408 \\\hline 4&166464\\4&16\\\hline 80 & ~~~~64 \\0&~~~~00\\\hline 808&~~6464\\8&~~6464\\ \hline &~~~~~0 \end{array}$

(vi) ​9548100

Sol :

$\begin{array}{r|l} &3090 \\\hline 3&9548100\\3&9\\\hline 60 & ~~54 \\0&~~00\\\hline 609&~~5481\\9&~~5481\\ \hline &~~~~~0 \end{array}$

(vii) ​$\dfrac{1089}{3481}$

Sol :

$=\frac{\sqrt{1089}}{\sqrt{3481}}$

$\begin{array}{r|l} &33 \\\hline 3&1089\\3&9\\\hline 63 & 189 \\3&189\\\hline &~~0 \end{array}$

$\begin{array}{r|l} &59 \\\hline 5&3481\\5&25\\\hline 109 & ~~981 \\9&~~981\\\hline &~~0 \end{array}$

$=\frac{33}{59}$

(viii) ​​​$\dfrac{7569}{14884}$

Sol :

​$=\frac{\sqrt{7569}}{\sqrt{14884}}$

$\begin{array}{r|l} &87 \\\hline 8&7569\\8&64\\\hline 167& 1169 \\17&1169\\\hline &~~0 \end{array}$

$\begin{array}{r|l} &122 \\\hline 1&14884\\1&1\\\hline 22& ~~48 \\2&~~44\\\hline &~~~~484\\&~~~~484\\ \hline &~~~~~~0 \end{array}$

$=\frac{87}{122}$

(ix) $2\dfrac{337}{9216}$

Sol :

$=\sqrt{\left(\frac{9216 \times 2+337}{9216}\right)}$

$=\sqrt{\frac{18769}{9216}}$

$=\frac{\sqrt{18769}}{{\sqrt{9216}}}$

$\begin{array}{r|l} &137 \\\hline 1&18769\\1&1\\\hline 23& ~~87 \\3&~~69\\\hline 267&~~1869\\7&~~1869\\\hline& ~~~~0 \end{array}$

$\begin{array}{r|l} &96 \\\hline 9&9216\\9&81\\\hline 186& ~~1116 \\6&~~1116\\\hline &~~~~0 \end{array}$

$=\frac{137}{96}=1\frac{41}{96}$

(x) ​$9\dfrac{4185}{5776}$​

Sol :

$=\sqrt{\frac{5776 \times 9+4185}{5776}}$

$=\sqrt{\frac{56169}{5776}}$

$=\frac{\sqrt{56169}}{\sqrt{5176}}$

$\begin{array}{r|l} &237 \\\hline 2&56169\\1&4\\\hline 43& 161 \\3&129\\\hline 467&~~3269\\7&~~3269\\\hline& ~~~~0 \end{array}$

$\begin{array}{r|l} &76\\\hline 7&5776\\7&49\\\hline 146& 876\\6&876\\\hline &~~0 \end{array}$

$=\frac{237}{76}$

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Q2 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 2

Find the perimeter of a square field whose area is 13689 m²

Sol :

Perimeter of square= 4×side

Area of square=side×side=side²

13689=side²

side=$\sqrt{13689}$

$\begin{array}{r|l} &117 \\\hline 1&13689\\1&1\\\hline 21& ~~36 \\1&~~21\\\hline 227&~~1589\\7&~~1589\\\hline& ~~~~0 \end{array}$

side=117

Perimeter of square=4×117=468

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Q3 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 3

What should be subtracted from 18246 to get a perfect square number ? What is this perfect square number ? Also, find its square root.

Sol :

$\begin{array}{r|l} &135 \\\hline 1&18246\\1&1\\\hline 23& ~~82 \\3&~~69\\\hline 265&~~1346\\5&~~1325\\\hline& ~~~~~~21 \end{array}$

As it can be seen that square of 135 is less than by 21 (remainder)

If we subtract the remainder 21 from the number 18.246, we get a perfect square.

∴Required perfect square=18246-21=18.225

Square root$=\sqrt{18225}=135$

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Question 4

What should be added to 14841 to make the sum a perfect square ?

Sol :

$\begin{array}{r|l} &121 \\\hline 1&14841\\1&1\\\hline 22& ~~48 \\2&~~44\\\hline 241&~~441\\1&~~241\\\hline& ~~~~~~200 \end{array}$

We observe that the given number is greater than square of 121 and less than square of 122. 

So, number to be added$=(122)^{2}-14841$

=14884-14841=43

Resulting number=14841+43=14884

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Q5 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 5

Find the least number which must be subtracted from 63520 to make it a perfect square.

Sol :

$\begin{array}{r|l} &252 \\\hline 2&63520\\2&4\\\hline 45& 235 \\5&225\\\hline 502&~~1020\\&~~1004\\ \hline &~~~~~~16 \end{array}$

As it can be seen that square of 252 is less than 63520 by 16 (remainder)

To make it a perfect square, we have to subtract=63520-16=63504

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Question 6

Find:

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

Sol :

The least six digit number is 100000

$\begin{array}{r|l} &316 \\\hline 3&100000\\3&9\\\hline 61& 100 \\1&~~61\\\hline 626&~~3900\\&~~3756\\ \hline &~~~~144 \end{array}$

We can see that square of 316 is less than 100000 by 144

Perfect square=100000-144

=99856=$(316)^2$

But it is not a six digit number.

So, we have to choose next one

$=(317)^2$

=100489

(ii) Find the greatest number of six digits which is a perfect square.

Sol :

The greatest six digit number is 999999

$\begin{array}{r|l} &999 \\\hline 9&999999\\9&81\\\hline 189& 1899 \\9&1701\\\hline 1989&~~19899\\9&~~17901\\ \hline &~~~~1998 \end{array}$

We can see that square of 999 is less than 999999 by 1998

∴Required perfect square=999999-1998

=998001

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Q7 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 7

A gardener arranges his plants in rows to form a perfect square. He finds that in doing so, 25 plants are left out.If the total number of plants be 2234 , find the numbers of plants in each row.

Sol :

Prefect square number=Total plants-Left out plants

=2234-25=2209

Number of plants in each row

$=\sqrt{2209}$

=47

$\begin{array}{r|l} &47 \\\hline 4&2209\\4&16\\\hline 87& 609 \\7&609\\\hline &~~0 \end{array}$

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Question 8

There are 800 children in a school. For a PT drill they have to stand in a square formation, such that the number of rows is equal to number of columns. Find the greatest number of children needed to complete the formation.

Sol :

Total number of student is 800

Given : Number of rows = Number of column=x

Required student t form a square=Number of rows ×Number of column

$=x^{2}=\sqrt{800}$

$\begin{array}{r|l} &28 \\\hline 2&800\\2&4\\\hline 48 & 400 \\8&384\\\hline &~~16 \end{array}$

We can see that square of 28 is less than 800 by 16

∴Required student=800-16=784

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MCQS

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Q9 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 9

Find the correct one:

The square root of 1585081 is

(a) 1259

(b) 2159

(c) 1251

(d) 1291

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Q10 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper

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Question 10

Find the value of 

​$\sqrt{240.25}+\sqrt{2.4025}+\sqrt{0.024025}+\sqrt{0.00024025}$​

(a) 1602205

(b) 16.2402

(c) 17.2205

(d) 155.2205