Question

If $m$is a cube root of $n,$ then $n$is

• A. $m^3$
• B. $\sqrt{m}$
• C. $\frac{m}{3}$
• D. $3\sqrt{m}$

Answer 1

The correct option is A

$m^3$

Solve for the required value

Given, $m$ is the cube root of $n$,i.e. $\sqrt[3]{n}=m$

Cubing on both sides, we get,

$$\begin{gathered} {\left(n^{\frac{1}{3}}\right)}^3=m^3 \\ \Rightarrow n^{\frac{1}{3}\times 3}=m^3\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \end{gathered}$$

$\Rightarrow$ $n=m^3$

Hence, the correct option is option (A) i.e. $m^3.$