Question

Find the nearest integer to the cube root of $46656$.

Answer 1

For finding the nearest integer to the cube root of $46656$, let us split $46656$ as $46$ and $656$

Now, $3^3=27<46<64=4^3$

$⟹{30}^3=27000<46656<64000={40}^3$

$⟹46656$ lies between ${30}^3$ and ${40}^3$

Now, $46656$ is closer to ${40}^3$ than ${30}^3$

Let us go for more accurate result

${39}^3=59319>46656,{38}^3=54872>46656,{37}^3=50653>46656$ and ${36}^3=46656$

Hence, the nearest integer to the cube root of $46656$ is $36$.