Question

What is the least number that should be subtracted from $1385$ to get a perfect square? Also find the square root of the perfect square.

Answer 1

Find the square root of the perfect square.

Long division can be used to find the square root of a given number, as demonstrated below:

To create a perfect square, the least number that should be removed from $1385$using the long division method is $16$.

Now,

$\begin{array}{rcl}\mathrm{Perfect}\mathrm{square}& =& 1385-16\\ & =& 1369\end{array}$

then,

$\begin{array}{rcl}\sqrt{1369}& =& \sqrt{\left(37\times 37\right)}\\ & =& \left(\sqrt{{37}^2}\right)\\ & =& 37\end{array}$

Hence, The perfect square number $1369$has a square root of $37$.