Question

Find the least number that must be subtracted from $5607$ so as to get a perfect square. Also, find the square root of the perfect square.

Answer 1

Let us try to find $\sqrt{5607}$ by long division method.

We get the remainder 131. This shows that $(74{)}^2$ is less than $5607$ by $131$.
This means if we subtract the remainder from the number we get a perfect square.

Therefore, the required perfect square is $5067-131=5467$ and $\sqrt{5476}=74$.