# How to simplify root(3)(24y^21x^5) ?

Apr 2, 2017

$2 x {y}^{7} \sqrt[3]{2 {x}^{2}}$

#### Explanation:

Write the radicand as aproduct of prime factors.

$\sqrt[3]{24 {y}^{21} {x}^{5}} = \sqrt[3]{3 \times {2}^{3} {y}^{21} {x}^{5}}$

Write cubes where possible:
$\sqrt[3]{3 \times {2}^{3} {y}^{21} {x}^{5}} = \sqrt[3]{3 \times \textcolor{red}{{2}^{3} {y}^{21} {x}^{3}} \times {x}^{2}}$

Find the cube roots where possible by dividing the indices by $3$.

$= \textcolor{red}{2 x {y}^{7}} \sqrt[3]{2 {x}^{2}}$