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.
(i) 402 (ii) 1989
(iii) 3250 (iv) 825
(v) 4000
(i) The square root of 402 can be calculated by long division method as follows.

20
2
40
02
00
2
The remainder is 2. It represents that the square of 20 is less than 402 by 2. Therefore, a perfect square will be obtained by subtracting 2 from the given number 402.
Therefore, required perfect square = 402 − 2 = 400
And,
(ii) The square root of 1989 can be calculated by long division method as follows.

44
4
84
389
336
53
The remainder is 53. It represents that the square of 44 is less than 1989 by 53. Therefore, a perfect square will be obtained by subtracting 53 from the given number 1989.
Therefore, required perfect square = 1989 − 53 = 1936
And,
(iii) The square root of 3250 can be calculated by long division method as follows.

57
5
107
750
749
1
The remainder is 1. It represents that the square of 57 is less than 3250 by 1. Therefore, a perfect square can be obtained by subtracting 1 from the given number 3250.
Therefore, required perfect square = 3250 − 1 = 3249
And,
(iv) The square root of 825 can be calculated by long division method as follows.

28
2
48
425
384
41
The remainder is 41. It represents that the square of 28 is less than 825 by 41. Therefore, a perfect square can be calculated by subtracting 41 from the given number 825.
Therefore, required perfect square = 825 − 41 = 784
And,
(v) The square root of 4000 can be calculated by long division method as follows.

63
6
123
400
369
31
The remainder is 31. It represents that the square of 63 is less than 4000 by 31. Therefore, a perfect square can be obtained by subtracting 31 from the given number 4000.
Therefore, required perfect square = 4000 − 31 = 3969
And,