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. $402$

Answer 1

Solve for the nearest perfect squares of $402$.

Given number is $402$

Few perfect squares around the given numbers are

$$\begin{gathered} 400<402<441 \\ {20}^2<402<{21}^2 \end{gathered}$$

Now, $402-400=2$

If we subtract $2$ from $402$, then the number becomes $400$ which is a perfect square of $20$.

Hence, the required least number is $2$ and is a perfect square of $20$.