# How do you simplify the cube root of 32?

Sep 18, 2015

#### Answer:

${2}^{\frac{5}{3}}$

#### Explanation:

I'm wondering if you could call this a "simplification" but here it is "rewritten" in another form:
since $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = {2}^{5}$,
we can write:
$\sqrt[3]{32} = \sqrt[3]{{2}^{5}} = {2}^{\frac{5}{3}}$
(because $\sqrt[3]{x} = {x}^{\frac{1}{3}}$)
or if one absolutely wants to get some integer out of the root, we could write:
$\sqrt[3]{32} = \sqrt[3]{8 \cdot 4} = \sqrt[3]{{2}^{3} \cdot 4} = 2 \sqrt[3]{4}$