Question

Question 5 (iii)
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

252

Answer 1

252

$\begin{array}{cc}& 15\\ 1& \overline{2}\overline{52}\\ & -1\\ 25& 152\\ & -125\\ & 27\end{array}$

Since remainder is 27. Therefore ${15}^2<252$

Next perfect square number ${16}^2=256$

Hence, number to be added = 256 – 252 =4

$\therefore 252+4=256$

Hence, the square root of 256 is 16.