# What is the cube root of 351?

May 22, 2018

$\sqrt[3]{351} = 3 \sqrt[3]{13} \approx 7.054$

#### Explanation:

When looking for the ${n}^{t h}$ root of integers it is often useful to express the integer as its prime factors.

In this case, $351 = 3 \times 3 \times 3 \times 13$

$\therefore \sqrt[3]{351} = \sqrt[3]{3 \times 3 \times 3 \times 13}$

Now, since $3$ appears three times in the factorisation we can take it through the root as follows,

$\sqrt[3]{351} = 3 \sqrt[3]{13}$

Since $\sqrt[3]{13}$ is irrational, the above result is the "exact value".

A decimal approximation can be found using a calculator.

$\sqrt[3]{351} \approx 7.054$