# How do you simplify: square root of (x^2 - 4x +4)?

Jul 19, 2015

$\sqrt{{x}^{2} - 4 x + 4} = \sqrt{{\left(x - 2\right)}^{2}} = \left\mid x - 2 \right\mid$

#### Explanation:

Note that ${x}^{2} - 4 x + 4 = {\left(x - 2\right)}^{2}$ has two square roots,
namely $\left(x - 2\right)$ and $- \left(x - 2\right)$.

Since we use sqrt to denote the positive square root, we need to pick whichever is non-negative of $\left(x - 2\right)$ and $- \left(x - 2\right)$.

We can express that as $\left\mid x - 2 \right\mid$