Question

Write the expression in simplest form.
`\sqrt{49 {x}^(5) }`

Answer 1

`=7x^2\sqrt[]{x}`

Explanation:

Given the expression:

`√(49x^5)`

First, the expression can be rewritten in the form below:

`\begin{gathered} =\sqrt[]{49* x^5} \\ By\text{ multiplication of surds: }=\sqrt[]{mn}=\sqrt[]{m}*\sqrt[]{n} \\ =\sqrt[]{49^{}}*\sqrt[]{x^5} \end{gathered}`

Next, we simplify:

`\begin{gathered} =\sqrt[]{7^2}*\sqrt[]{x^4* x} \\ =7*\sqrt[]{x^4}*\sqrt[]{x} \\ =7* x^2*\sqrt[]{x} \end{gathered}`

The simplest form of the expression is:

`=7x^2\sqrt[]{x}`