# How do you simplify sqrt3(sqrt27-sqrt3)?

May 8, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as:

$\left(\sqrt{3} \cdot \sqrt{27}\right) - \left(\sqrt{3} \cdot \sqrt{3}\right)$

Next, use this rule for multiplying radicals to again rewrite the expression as:

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

$\left(\sqrt{3} \cdot \sqrt{27}\right) - \left(\sqrt{3} \cdot \sqrt{3}\right) = \sqrt{3 \cdot 27} - \sqrt{3 \cdot 3} \implies$

$\sqrt{81} - \sqrt{9} \implies 9 - 3 \implies 6$