# How do you evaluate 2 square root of 3 - 4 square root of 2 + 6 square root of 3 + 8 square root of 2?

Mar 15, 2016

$8 \sqrt{3} + 4 \sqrt{2}$

#### Explanation:

$1$. Recall that you can add and subtract radicals if they have the same value in the square root sign. You can think of the $\textcolor{t e a l}{\text{radical}}$ as a $\textcolor{t e a l}{\text{variable}}$. Thus, start by grouping all like terms together.

$\textcolor{red}{2} \textcolor{t e a l}{\sqrt{3}}$ $\textcolor{\mathmr{and} a n \ge}{- 4} \textcolor{t e a l}{\sqrt{2}}$ $\textcolor{b l u e}{+ 6} \textcolor{t e a l}{\sqrt{3}}$ $\textcolor{p u r p \le}{+ 8} \textcolor{t e a l}{\sqrt{2}}$

$= \textcolor{red}{2} \textcolor{t e a l}{\sqrt{3}}$ $\textcolor{b l u e}{+ 6} \textcolor{t e a l}{\sqrt{3}}$ $\textcolor{\mathmr{and} a n \ge}{- 4} \textcolor{t e a l}{\sqrt{2}}$ $\textcolor{p u r p \le}{+ 8} \textcolor{t e a l}{\sqrt{2}}$

$2$. Add/subtract as appropriate.

=(color(red)2 color(blue)(+6))color(teal)(sqrt(3))+(color(orange)(-4) color(purple)(+8))color(teal)(sqrt(2))

$3$. Simplify.

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 8 \sqrt{3} + 4 \sqrt{2} \textcolor{w h i t e}{\frac{a}{a}} |}}}$