Question

Use the properties of radicals to simplify the expression​

Answer 1

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.