Question

Find the least number which must be added to each of the following numbers so as to get a perfect square. $6412$

Answer 1

Find the nearest perfect squares of $6412$

Given number is $6412$

Few perfect squares around the given number can be seen as,

$$\begin{gathered} 6400<6412<6561 \\ {80}^2<6412<{81}^2 \end{gathered}$$

$\because 6561-6412=149$

Hence, If we add $149$ to $6412$, then the number becomes $6412+149=6561$ which is a perfect square of $81$.

Hence, the required least number is $149$ and number formed will be a perfect square of $81$.