Question

Find the nearest integer to the cube root of $331776$:

Answer 1

For finding the nearest integer to the cube root of $331776$, let us split $331776$ as $331$ and $776$

Now, $6^3=216<331<343=7^3$

$⟹{60}^3=216000<331776<343000={70}^3$

$⟹331776$ lies between ${60}^3$ and ${70}^3$

Now, $331776$ is closer to ${70}^3$ than ${60}^3$

Let us go for more accurate result

${69}^3=328509<331667<343000={70}^3$

Here, $331667-328509=3267$ and $343000-331776=11224$

Thus, $331667$ is closer to ${69}^3$.

Hence, the nearest integer to the cube root of $331776$ is $69$.