# How do you simplify sqrt(18 x^8)?

Mar 10, 2016

$\sqrt{18 {x}^{8}} = 3 \sqrt{2} {x}^{4}$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

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Notice that $18 = 2 \cdot 3 \cdot 3 = 2 \cdot {3}^{2}$

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Note also that $3 {x}^{4} \ge 0$ for all $x \in \mathbb{R}$

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Hence:

$\sqrt{18 {x}^{8}} = \sqrt{{\left(3 {x}^{4}\right)}^{2} \cdot 2} = \sqrt{{\left(3 {x}^{4}\right)}^{2}} \sqrt{2} = 3 {x}^{4} \sqrt{2} = 3 \sqrt{2} {x}^{4}$