# How do you simplify 5sqrt3(6sqrt10-6sqrt3)?

Jun 21, 2018

$30 \left(\sqrt{30} - 3\right)$

#### Explanation:

We essentially have the following

$\textcolor{b l u e}{5} \textcolor{\lim e}{\sqrt{3}} \cdot \textcolor{b l u e}{6} \textcolor{\lim e}{\sqrt{10}} - \textcolor{b l u e}{5} \textcolor{\lim e}{\sqrt{3}} \cdot \textcolor{b l u e}{6} \textcolor{\lim e}{\sqrt{3}}$

Which can be simplified if we multiply the integers and square roots together, respectively. We'll get

$\textcolor{b l u e}{\left(5 \cdot 6\right)} \textcolor{\lim e}{\sqrt{3} \sqrt{10}} - \textcolor{b l u e}{\left(5 \cdot 6\right)} \textcolor{\lim e}{\sqrt{3} \sqrt{3}}$

Which simplifies to

$\textcolor{b l u e}{30} \textcolor{\lim e}{\sqrt{30}} - \textcolor{b l u e}{30} \cdot \textcolor{\lim e}{3}$

$\implies \textcolor{b l u e}{30} \textcolor{\lim e}{\sqrt{30}} - 90$

Since $30$ has no perfect square factors, we cannot simplify the radical any further. We can factor a $30$ out of both terms, however. We get

$30 \left(\sqrt{30} - 3\right)$

Hope this helps!