# How do you simplify sqrt3 (7- sqrt3)?

Aug 3, 2016

$7 \sqrt{3} - 3$

#### Explanation:

Apply the $\textcolor{b l u e}{\text{distributive law.}}$ That is multiply each term inside the bracket by $\sqrt{3}$

$\textcolor{red}{\sqrt{3}} \left(7 - \sqrt{3}\right) = \left(\textcolor{red}{\sqrt{3}} \times 7\right) - \left(\textcolor{red}{\sqrt{3}} \times \sqrt{3}\right)$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sqrt{a} \times \sqrt{a} = {\left(\sqrt{a}\right)}^{2} = a} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \left(\textcolor{red}{\sqrt{3}} \times 7\right) - \left(\textcolor{red}{\sqrt{3}} \times \sqrt{3}\right) = 7 \sqrt{3} - 3$