Question -
Answer -
(i)
Here remainder is 41
It represents that square of 22 is less than 525.
Next number is 23 an 232 = 529
Hence, the number to be added = 529 – 525 = 4
New number = 529
Thus, √529 = 23
(ii)
Here the remainder is 69
It represents that square of 41 is less than in 1750.
The next number is 42 and 422 = 1764
Hence, number to be added to 1750 = 1764 – 1750 = 14
Require perfect square = 1764
√1764 = 42
(iii)
Here the remainder is 27.
It represents that a square of 15 is less than 252.
The next number is 16 and 162 = 256
Hence, number to be added to 252 = 256 – 252 = 4
New number = 252 + 4 = 256
Required perfect square = 256
and √256 = 16
(iv)
The remainder is 61.
It represents that square of 42 is less than in 1825.
Next number is 43 and 432 = 1849
Hence, number to be added to 1825 = 1849 – 1825 = 24
The required perfect square is 1848 and √1849 =43
(v)
Here, the remainder is 12.
It represents that a square of 80 is less than in 6412.
The next number is 81 and 812 = 6561
Hence the number to be added = 6561 – 6412 = 149
The require perfect square is 6561 and √6561 = 81