# How do you simplify sqrt(121x^10)?

Nov 7, 2015

$\sqrt{121 {x}^{10}} = 11 {\left\mid x \right\mid}^{5}$

#### Explanation:

If $a \ge 0$ then $\sqrt{{a}^{2}} = a$

For any $a \in \mathbb{R}$, ${\left(- a\right)}^{2} = {a}^{2}$

Hence: $\sqrt{{a}^{2}} = \left\mid a \right\mid$ for all $a \in \mathbb{R}$

So:

$\sqrt{121 {x}^{10}} = \sqrt{{\left(11 {x}^{5}\right)}^{2}} = \left\mid 11 {x}^{5} \right\mid = 11 {\left\mid x \right\mid}^{5}$