# Question #acf06

Feb 24, 2018

Answer: $5 {\left(x + 2\right)}^{2}$

#### Explanation:

Assuming question is asking for $\sqrt{25 {\left(x + 2\right)}^{4}}$

By definition of square root, we know that:
$\sqrt{{p}^{2}} = p$, where $p$ is any function

Therefore, applying this definition to the original problem we can see that the original problem can be factored into the form ${p}^{2}$:
$\sqrt{25 {\left(x + 2\right)}^{4}}$
$= \sqrt{5 \cdot 5 \cdot {\left(x + 2\right)}^{2} \cdot {\left(x + 2\right)}^{2}}$
$= \sqrt{{5}^{2} \cdot {\left({\left(x + 2\right)}^{2}\right)}^{2}}$
$= \sqrt{{\left(5 {\left(x + 2\right)}^{2}\right)}^{2}}$

Now, we can set our $p$ to be $p = 5 {\left(x + 2\right)}^{2}$, so our answer is
$5 {\left(x + 2\right)}^{2}$