Use the properties of radicals to simplify the expression

Question

asked Jan 18, 2022 214k views

1 Answer

Bowery · Answer 1 · 2022-01-22T22:01:06+0000

Given:

The expression is

$\frac{\sqrt[3]{9}}{\sqrt[3]{4}}$

To find:

The simplified form of given expression.

Solution:

We have,

$\frac{\sqrt[3]{9}}{\sqrt[3]{4}}$

It can be written as

$\frac{\sqrt[3]{9}}{\sqrt[3]{4}}=\sqrt[3]{(9)/(4)}$
$\left[\because \frac{\sqrt[a]{x}}{\sqrt[a]{y}}=\sqrt[a]{(x)/(y)}\right]$

Therefore, the simplified form of given expression is
$\sqrt[3]{(9)/(4)}$ .

Note: We can further simplify this expression but be need use exponential properties.