Exercise 3D
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
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
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
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
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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