# How do you simplify 4root3(135)?

May 1, 2017

See the solution process below:

#### Explanation:

We can use this rule for radicals to rewrite the expression:

$\sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$

$4 \sqrt[3]{135} = 4 \sqrt[3]{27 \cdot 5} = 4 \sqrt[3]{27} \sqrt[3]{5}$

We can now simplify $\sqrt[3]{27} = 3$ to write:

$4 \sqrt[3]{27} \sqrt[3]{5} = \left(4 \cdot 3\right) \sqrt[3]{5} = 12 \sqrt[3]{5}$