Answer :

(i) The square root of 525 can be calculated by long division method as:

The remainder is 41

It represents that the square of 22 is less than 525

Next number is 23 and 23^{2} = 529

Hence, number to be added to 525 = 23^{2} - 525

= 529 - 525

= 4

The required perfect square is 529 and = 23

(ii) The square root of 1750 can be calculated by long division method as follows:

The remainder is 69

It represents that the square of 41 is less than 1750

The next number is 42 and 42^{2} = 1764

Hence, number to be added to 1750 = 42^{2}– 1750

= 1764 - 1750

= 14

The required perfect square is 1764 and = 42

(iii) The square root of 252 can be calculated by long division method as follows:

The remainder is 27. It represents that the square of 15 is less than 252

The next number is 16 and 16^{2} = 256

Hence, number to be added to 252 = 16^{2} - 252

= 256 - 252

= 4

The required perfect square is 256 and = 16

(iv) The square root of 1825 can be calculated by long division method as follows:

The remainder is 61. It represents that the square of 42 is less than 1825

The next number is 43 and 43^{2} = 1849

Hence, number to be added to 1825 = 43^{2} - 1825

= 1849- 1825

= 24

Hence, number to be added to 1825 = 24

The required perfect square is 1849 and = 43

(v) The square root of 6412 can be calculated by long division method as follows:

The remainder is 12. It represents that the square of 80 is less than 6412

The next number is 81 and 81^{2} = 6561

Hence, number to be added to 6412= 81^{2} - 6412

= 6561- 6412

= 149

Hence, number to be added to 6412= 149

The required perfect square is 6561 and = 81

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Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics

Using square rootRD Sharma - Mathematics