Question

Find the nearest integer to the square root of $824.$

Answer 1

We know, ${28}^2=784$ and ${29}^2=841$
Also, we have, $784<824<841$
$⟹{28}^2<824<{29}^2$

Difference of $784$ and $824$ is $40$ whereas difference of $824$ and $841$ is $17$.
So, the square root of $824$ is nearest to $29$.

Hence, the answer is $29$.