Question

Find the nearest integer to the square root of $1729.$

Answer 1

We know, ${41}^2=1681$ and ${42}^2=1764$
Also, we have, $1681<1729<1764$
$⟹{41}^2<1729<{42}^2$

Difference of $1681$ and $1729$ is $48$ whereas difference of $1729$ and $1764$ is $35$.
So, the square root of $1729$ is nearest to $42$.

Hence, the answer is $42$.