# How do you multiply radical expressions?

Mar 22, 2015

One method is to make one big radical, then simplify.

$\sqrt[3]{2 {x}^{2} {y}^{6}} \sqrt[3]{20 x {y}^{4}} = \sqrt[3]{2 {x}^{2} {y}^{6} \cdot 20 {x}^{2} {y}^{4}}$

$= \sqrt[3]{40 {x}^{3} {y}^{10}} = \sqrt[3]{8 \cdot 5 {x}^{3} {y}^{9} y} = 2 x {y}^{3} \sqrt[3]{5 y}$

Or simplify first, then combine what's left and simplify again:

$\sqrt[3]{2 {x}^{2} {y}^{6}} \sqrt[3]{20 x {y}^{4}} = \left[{y}^{2} \sqrt[3]{2 {x}^{2}}\right] \left[y \sqrt[3]{20 x y}\right]$

$= {y}^{3} \sqrt[3]{40 {x}^{3} y} = 2 x {y}^{3} \sqrt[3]{5 y}$.