Question

Question 4 (iv)
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:

825

Answer 1

825

$\begin{array}{cc}& 28\\ 2& \overline{8}\overline{25}\\ & -4\\ 48& 425\\ & -384\\ & 41\end{array}$

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

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.

$\therefore 825-41=784$

$\begin{array}{cc}& 28\\ 2& \overline{7}\overline{84}\\ & -4\\ 48& 384\\ & -384\\ & 0\end{array}$

Hence, the square root of 784 is 28.