# How do you simplify 5sqrt(54) ?

Mar 5, 2017

$5 \sqrt{54} = 15 \sqrt{6}$

#### Explanation:

Note that if $a , b \ge 0$ we have:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$

Factor $54$ to identify square factors:

$54 = 2 \cdot {3}^{3} = {3}^{2} \cdot 6$

Hence:

$5 \sqrt{54} = 5 \sqrt{{3}^{2} \cdot 6} = 5 \sqrt{{3}^{2}} \sqrt{6} = 5 \cdot 3 \sqrt{6} = 15 \sqrt{6}$

This is the simplest form of the square root.