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Question

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained.
525
1750

A
4,23;14,48
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B
4,27;14,42
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C
4,23;14,42
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D
4,27;14,48
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Solution

The correct option is C 4,23;14,42
We try to find out the square root of 525.
22¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2¯5¯254¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯4212584–––––41
We observe that
(22)2<525<(23)2
The required number to be added
=(23)2525
=529525=4
Required perfect square number
=525+4=529
Clearly, 529=23.
We try to find out the square root of 1750
41¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯4¯17¯5016¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯8115081–––––69
We observe that (41)2<1750<(42)2.
The required number to be added
=(42)21750
=17641750
=14
Required perfect square number
=(1750+14)=1764
Clearly, 1764=42.

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