Question

Question 4 (i)
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:

402

Answer 1

402

$\begin{array}{cc}& 20\\ 2& \overline{4}\overline{02}\\ & -4\\ 40& 02\\ & -00\\ & 2\end{array}$

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

Here, we get remainder 2. Therefore 2 must be subtracted from 402 to get a perfect square.

$\begin{array}{cc}& 20\\ 2& \overline{4}\overline{00}\\ & -4\\ 00& 00\\ & -00\\ & 0\end{array}$

Hence, the square root of 400 is 20.