# What is the square root of 32^(2/3)?

Sep 19, 2015

$2 \sqrt[3]{4}$

#### Explanation:

${\sqrt{32}}^{\frac{2}{3}}$

$= {\left[{\left(32\right)}^{\frac{2}{3}}\right]}^{\frac{1}{2}}$

$= {\left(32\right)}^{\frac{2}{3} \cdot \frac{1}{2}}$

$= {\left(32\right)}^{\frac{1}{3}}$

$= {\left({2}^{5}\right)}^{\frac{1}{3}}$

$= \sqrt[3]{{2}^{5}}$

$= \sqrt[3]{{2}^{3} \cdot {2}^{2}}$

$= 2 \sqrt[3]{4}$

Sep 19, 2015

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

#### Explanation:

sqrt(32^(2/3))=sqrt((2^5)^(2/3)

sqrt((2^5)^(2/3))=sqrt(2^(10/3)

$\sqrt{{2}^{\frac{10}{3}}} = {\left({2}^{\frac{10}{3}}\right)}^{\frac{1}{2}}$

${\left({2}^{\frac{10}{3}}\right)}^{\frac{1}{2}} = {2}^{\frac{10}{6}}$

${2}^{\frac{10}{6}} = {2}^{\frac{5}{3}}$

${2}^{\frac{5}{3}} = {2}^{1 + \frac{2}{3}} = 2 \times {2}^{\frac{2}{3}}$

I hope that helps :)