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,