Question

Find the cube root of $-12$.

Answer 1

Calculate the prime factors:

The given number is $-12$.

In order to find the cube root of $-12$, first, we need to calculate the prime factors of $12$.

$\begin{array}{cc}2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$

So, $12=2\times 2\times 3$

Since no prime factor of $12$ is forming a triplet.

Therefore, no prime factor can be brought out of the cube root.

i.e., $\sqrt[3]{12}=\sqrt[3]{2\times 2\times 3}$

So, the cube root of $12$ is $\sqrt[3]{12}$.

It implies that the cube root of $\left(-12\right)$ is $\sqrt[3]{-12}$.

Hence, the cube root of $-12$ is $\sqrt[3]{-12}$.