# How do you simplify (2sqrt7+ sqrt3)(3sqrt7 + √2)?

Oct 13, 2017

$14 + 2 \sqrt{14} + 3 \sqrt{21} + \sqrt{6}$

#### Explanation:

$\left(\textcolor{red}{2 \sqrt{7}} + \textcolor{g r e e n}{\sqrt{3}}\right) \left(\textcolor{b l u e}{3 \sqrt{7}} + \textcolor{\mathmr{and} a n \ge}{\sqrt{2}}\right)$

Multiply every term in the first brackets to every term in the second bracket.

$= \textcolor{red}{2 \sqrt{7}} \cdot \textcolor{b l u e}{3 \sqrt{7}} + \textcolor{red}{2 \sqrt{7}} \textcolor{\mathmr{and} a n \ge}{\sqrt{2}} + \textcolor{b l u e}{3 \sqrt{7}} \textcolor{g r e e n}{\sqrt{3}} + \textcolor{\mathmr{and} a n \ge}{\sqrt{2}} \textcolor{g r e e n}{\sqrt{3}}$

$= 6 \times 7 + 2 \sqrt{7 \times 2} + 3 \sqrt{7 \times 3} + \sqrt{2 \times 3}$

$= 42 + 2 \sqrt{14} + 3 \sqrt{21} + \sqrt{6}$

As there are no like terms, this is the final answer $\uparrow$.