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

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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