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Question

Question 4 (iv)
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

825

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Solution

825

282¯¯¯8 ¯¯¯¯¯¯2544842538441

We know that, of we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.

82541=784

282¯¯¯7 ¯¯¯¯¯¯844483843840

Hence, the square root of 784 is 28.


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