Question

Use the properties of radicals to simplify the expression​

Answer 1

Given:

The expression is

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

To find:

The simplified form of given expression.

Solution:

We have,

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

It can be written as

$\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}=\sqrt[3]{\dfrac{9}{4}}$                    $\left[\because \dfrac{\sqrt[a]{x}}{\sqrt[a]{y}}=\sqrt[a]{\dfrac{x}{y}}\right]$

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

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