Question

Write the expression in simplest form.$\sqrt{49 {x}^{5} }$

Answer 1

Answer:

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

Explanation:

Given the expression:

$\sqrt{49x^5}$

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

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

Next, we simplify:

$\begin{gathered} =\sqrt[]{7^2}\times\sqrt[]{x^4\times x} \\ =7\times\sqrt[]{x^4}\times\sqrt[]{x} \\ =7\times x^2\times\sqrt[]{x} \end{gathered}$

The simplest form of the expression is:

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