Find the least number which must be added to each of the following number so as to get a perfect square.
525

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Solution

The square root of 525 has divisor 22 and remainder is 41
The next number is 23, 23^2 = 529
Number to be added to 525 is, $23^{2} - 525 = 4$
Thus, required perfect square is $\sqrt{529} = 23$

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Q. Find the least number which must be added to each of the following numbers so as to get a perfect square:
(i)

525

(ii)

1750

(iii)

252

(iv)

1825

(v)

6412

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.

(i) 525 (ii) 1750

(iii) 252 (iv) 1825

(v) 6412

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Find the least number which must be added to each of the following number so as to get a perfect square. 525

The square root of 525 has divisor 22 and remainder is 41The next number is 23, 23^2 = 529Number to be added to 525 is, 232−525=4Thus, required perfect square is √529=23

Find the least number which must be added to each of the following number so as to get a perfect square.
525

The square root of 525 has divisor 22 and remainder is 41
The next number is 23, 23^2 = 529
Number to be added to 525 is, $23^{2} - 525 = 4$
Thus, required perfect square is $\sqrt{529} = 23$