# How do you simplify the expression 5 sqrt(x^2)?

Mar 7, 2017

$5 \sqrt{{x}^{2}} = 5 x$ See a solution process below using rules of radicals and exponents:

#### Explanation:

First, use this rule of radicals to rewrite this expression:

$\sqrt[\textcolor{red}{n}]{x} = {x}^{\frac{1}{\textcolor{red}{n}}}$

$5 \sqrt{{x}^{2}} = 5 \sqrt[\textcolor{red}{2}]{{x}^{2}} = 5 {\left({x}^{2}\right)}^{\frac{1}{\textcolor{red}{2}}}$

Next, use this rule of exponents to further simplify:

$5 {\left({x}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{2}}} = 5 {x}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{2}}} = 5 {x}^{1}$

Now, we can complete the simplification using this rule of exponents:

${a}^{\textcolor{red}{1}} = a$

$5 {x}^{\textcolor{red}{1}} = 5 x$