# What is the sqrt(3xy)sqrt(27xy^3)?

Apr 6, 2018

The simplified expression is $9 x {y}^{2}$.

#### Explanation:

When you have two radicals multiplied together, you can multiply their radicands (the stuff under the radical sign):

$\textcolor{w h i t e}{=} \sqrt{\textcolor{red}{3} \textcolor{b l u e}{x} \textcolor{g r e e n}{y}} \cdot \sqrt{\textcolor{red}{27} \textcolor{b l u e}{x} \textcolor{g r e e n}{{y}^{3}}}$

$= \sqrt{\textcolor{red}{3} \textcolor{b l u e}{x} \textcolor{g r e e n}{y} \cdot \textcolor{red}{27} \textcolor{b l u e}{x} \textcolor{g r e e n}{{y}^{3}}}$

$= \sqrt{\textcolor{red}{3} \cdot \textcolor{b l u e}{x} \cdot \textcolor{g r e e n}{y} \cdot \textcolor{red}{27} \cdot \textcolor{b l u e}{x} \cdot \textcolor{g r e e n}{{y}^{3}}}$

$= \sqrt{\textcolor{red}{3} \cdot \textcolor{red}{27} \cdot \textcolor{b l u e}{x} \cdot \textcolor{b l u e}{x} \cdot \textcolor{g r e e n}{y} \cdot \textcolor{g r e e n}{{y}^{3}}}$

$= \sqrt{\textcolor{red}{81} \cdot \textcolor{b l u e}{{x}^{2}} \cdot \textcolor{g r e e n}{{y}^{4}}}$

$= \sqrt{\textcolor{red}{81}} \cdot \sqrt{\textcolor{b l u e}{{x}^{2}}} \cdot \sqrt{\textcolor{g r e e n}{{y}^{4}}}$

$= \textcolor{red}{9} \cdot \sqrt{\textcolor{b l u e}{{x}^{2}}} \cdot \sqrt{\textcolor{g r e e n}{{y}^{4}}}$

$= \textcolor{red}{9} \cdot \textcolor{b l u e}{x} \cdot \sqrt{\textcolor{g r e e n}{{y}^{4}}}$

$= \textcolor{red}{9} \cdot \textcolor{b l u e}{x} \cdot \textcolor{g r e e n}{{y}^{2}}$

$= \textcolor{red}{9} \textcolor{b l u e}{x} \textcolor{g r e e n}{{y}^{2}}$

That's the simplified expression. Hope this helped!