Question

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

Find the nearest perfect squares of $4000$.

Few of the perfect squares around the given number are:

$$\begin{gathered} 3969<4000<4096 \\ {63}^2<4000<{64}^2 \end{gathered}$$

$\because 4000-31=3969$

Hence, If we subtract $31$ from $4000$, then the number becomes $3969$ which is a perfect square of $63$.

Hence, the required least number is $31$ and the number obtained is square root of $63$.