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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

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(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,...
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(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,

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