Question

Question 4 (iii)
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:

3250

Answer 1

3250

$\begin{array}{cc}& 57\\ 5& \overline{32}\overline{50}\\ & -25\\ 107& 750\\ & -749\\ & 1\end{array}$

We know that, of we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square.

$\therefore 3250-1=3249$

$\begin{array}{cc}& 57\\ 5& \overline{32}\overline{49}\\ & -25\\ 107& 749\\ & -749\\ & 0\end{array}$

Hence, the square root of 3249 is 57.