How do you simplify -4sqrt(7/8)?

Apr 2, 2018

The expression simplifies to $- \sqrt{14}$.

Explanation:

$\textcolor{w h i t e}{=} - 4 \sqrt{\frac{7}{8}}$

$= - 4 \cdot \sqrt{\frac{7}{8}}$

$= - 4 \cdot \frac{\sqrt{7}}{\sqrt{8}}$

$= - 4 \cdot \frac{\sqrt{7}}{\sqrt{4 \cdot 2}}$

$= - 4 \cdot \frac{\sqrt{7}}{\sqrt{4} \cdot \sqrt{2}}$

$= - 4 \cdot \frac{\sqrt{7}}{2 \cdot \sqrt{2}}$

$= - 4 \cdot \frac{\sqrt{7}}{2 \cdot \sqrt{2}} \textcolor{red}{\cdot \frac{\sqrt{2}}{\sqrt{2}}}$

$= - 4 \cdot \frac{\sqrt{7} \cdot \sqrt{2}}{2 \cdot \sqrt{2} \cdot \sqrt{2}}$

$= - 4 \cdot \frac{\sqrt{7} \cdot \sqrt{2}}{2 \cdot {\left(\sqrt{2}\right)}^{2}}$

$= - 4 \cdot \frac{\sqrt{7} \cdot \sqrt{2}}{2 \cdot 2}$

$= - 4 \cdot \frac{\sqrt{7} \cdot \sqrt{2}}{4}$

$= - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \cdot \frac{\sqrt{7} \cdot \sqrt{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}$

$= - \sqrt{7} \cdot \sqrt{2}$

$= - \sqrt{14}$

We can verify this answer using a calculator:

Hope this helped!