Question

Question 4 (v)
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:

4000

Answer 1

4000

$\begin{array}{cc}& 63\\ 6& \overline{40}\overline{00}\\ & -36\\ 123& 400\\ & -369\\ & 31\end{array}$

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

Here, we get remainder 31. Therefore 31 must be subtracted from 825 to get a perfect square.

$\therefore 4000-31=3969$

$\begin{array}{cc}& 63\\ 6& \overline{39}\overline{69}\\ & -36\\ 123& 369\\ & -369\\ & 0\end{array}$

Hence, the square root of 3969 is 63.