Question:
If $m$ is the cube root of $n$, then $n$ is
(a) $m^{3}$
(b) $\sqrt{m}$
(c) $\frac{m}{3}$
(d) $\sqrt[3]{m}$
Solution:
(a) Given, $m$ is the cube root of $n$, i.e. $m=\sqrt[3]{n}$
$\Rightarrow \quad m=(n)^{1 / 3}$
$\Rightarrow \quad m^{3}=(n)^{3 / 3}$ [taking cube on both sides]
$\therefore \quad m^{3}=n$
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