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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.5251750

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;14,42We try to find out the square root of 525.22¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2∣¯5¯25∣−4¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯42∣125∣−84–––––––∣41We observe that(22)2<525<(23)2The required number to be added=(23)2−525=529−525=4∴ Required perfect square number=525+4=529Clearly, √529=23.We try to find out the square root of 175041¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯4∣¯17¯50∣−16¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯81∣150∣−81–––––––∣69We observe that (41)2<1750<(42)2.The required number to be added=(42)2−1750=1764−1750=14∴ Required perfect square number=(1750+14)=1764Clearly, √1764=42.

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