# How do you simplify (3sqrt11+3sqrt15)(3sqrt3-2sqrt2)?

Apr 26, 2017

$9 \sqrt{33} - 6 \sqrt{22} + 27 \sqrt{5} - 6 \sqrt{30}$

#### Explanation:

$\left(\textcolor{red}{3 \sqrt{11} \textcolor{g r e e n}{+ 3 \sqrt{15}}}\right) \left(\textcolor{b l u e}{3 \sqrt{3}} \textcolor{b r o w n}{- 2 \sqrt{2}}\right)$

Multiply each term in the bracket with each other term in the other bracket

$\textcolor{red}{3 \sqrt{11}} \left(\textcolor{b l u e}{3 \sqrt{3}}\right) + \textcolor{red}{3 \sqrt{11}} \left(\textcolor{b r o w n}{- 2 \sqrt{2}}\right) + \textcolor{g r e e n}{3 \sqrt{15}} \left(\textcolor{b l u e}{3 \sqrt{3}}\right) + \textcolor{g r e e n}{3 \sqrt{15}} \left(\textcolor{b r o w n}{- 2 \sqrt{2}}\right)$

Multiply the whole number with the whole number and the square root with the square root

$\textcolor{red}{3} \cdot \textcolor{b l u e}{3} \sqrt{\textcolor{red}{11} \cdot \textcolor{b l u e}{3}} + \textcolor{red}{3} \cdot \textcolor{b r o w n}{- 2} \sqrt{\textcolor{red}{11} \cdot \textcolor{b r o w n}{2}} + \textcolor{g r e e n}{3} \cdot \textcolor{b l u e}{3} \sqrt{\textcolor{g r e e n}{15} \cdot \textcolor{b l u e}{3}} + \textcolor{g r e e n}{3} \cdot \textcolor{b r o w n}{- 2} \sqrt{\textcolor{g r e e n}{15} \cdot \textcolor{b r o w n}{2}}$

$9 \sqrt{33} - 6 \sqrt{22} + 9 \sqrt{45} - 6 \sqrt{30}$

$9 \sqrt{45}$ can be simplified

$9 \sqrt{45} = 9 \cdot \sqrt{3 \cdot 3 \cdot 5} = 9 \cdot \sqrt{{3}^{2} \cdot 5} = 9 \cdot \sqrt{{3}^{2}} \cdot \sqrt{5} = 9 \cdot 3 \sqrt{5} = 27 \sqrt{5}$

So $9 \sqrt{33} - 6 \sqrt{22} + \textcolor{m a \ge n t a}{9 \sqrt{45}} - 6 \sqrt{30}$ can be rewritten as

$9 \sqrt{33} - 6 \sqrt{22} + \textcolor{m a \ge n t a}{27 \sqrt{5}} - 6 \sqrt{30}$

These numbers can't be combined due to different numbers inside the roots, so this is the final answer.