# What is the square root of: x^2 + 4x + 4?

Apr 29, 2018

The square root equals $x + 2$.

#### Explanation:

First, factor the expression under the radical:

$\textcolor{w h i t e}{=} \sqrt{{x}^{2} + 4 x + 4}$

$= \sqrt{{x}^{2} + 2 x + 2 x + 4}$

$= \sqrt{\textcolor{red}{x} \left(x + 2\right) + 2 x + 4}$

$= \sqrt{\textcolor{red}{x} \left(x + 2\right) + \textcolor{b l u e}{2} \left(x + 2\right)}$

$= \sqrt{\left(\textcolor{red}{x} + \textcolor{b l u e}{2}\right) \left(x + 2\right)}$

$= \sqrt{{\left(x + 2\right)}^{2}}$

$= x + 2$

That's the simplification. Hope this helped!