# How would you simplify sqrt 7 (3-sqrt 7)+8 sqrt7?

Mar 15, 2016

$11 \sqrt{7} - 7$

#### Explanation:

$1$. Distribute the $\sqrt{7}$ to each term in the brackets.

$\textcolor{red}{\sqrt{7}} \left(3 - \sqrt{7}\right) + 8 \sqrt{7}$

$= \textcolor{red}{\sqrt{7}} \cdot 3 - \sqrt{7 \textcolor{red}{\cdot 7}} + 8 \sqrt{7}$

$= 3 \sqrt{7} - 7 + 8 \sqrt{7}$

$2$. Since radicals are like variables, you can think of $\textcolor{b l u e}{\sqrt{7}}$ in $3 \textcolor{b l u e}{\sqrt{7}}$ as a $\textcolor{b l u e}{\text{variable}}$. Thus, add $8 \sqrt{7}$ to $3 \sqrt{7}$.

$= 3 \sqrt{7} + 8 \sqrt{7} - 7$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 11 \sqrt{7} - 7 \textcolor{w h i t e}{\frac{a}{a}} |}}}$