How do you simplify 4 *sqrt(3/4)?

Jul 10, 2018

color(crimson)( => 2 sqrt 3

Explanation:

$4 \cdot \sqrt{\frac{3}{4}}$

$\implies {\left(\sqrt{4}\right)}^{2} \cdot \frac{\sqrt{3}}{\sqrt{4}}$

$\implies \sqrt{4} \cdot \cancel{\sqrt{4}} \cdot \frac{\sqrt{3}}{\cancel{\sqrt{4}}}$

$\implies \sqrt{4} \cdot \sqrt{3}$

color(crimson)( => 2 sqrt 3

Jul 10, 2018

$2 \sqrt{3}$

Explanation:

$4 \cdot \sqrt{\frac{3}{4}}$

$4 \cdot \frac{\sqrt{3}}{\sqrt{4}}$

$4 \cdot \frac{\sqrt{3}}{\sqrt{4}} \times \frac{\sqrt{4}}{\sqrt{4}}$

$4 \cdot \frac{\sqrt{3} \times \sqrt{4}}{\sqrt{4} \times \sqrt{4}}$

$4 \cdot \frac{\sqrt{12}}{4}$

$\cancel{4} \cdot \frac{\sqrt{12}}{\cancel{4}}$

$\sqrt{12}$

$\sqrt{3 \times 4}$

$\sqrt{3} \times \sqrt{4}$

$\sqrt{3} \times 2$

$2 \sqrt{3}$

Jul 10, 2018

color(blue)(=> 2 sqrt3

Explanation:

$4 \cdot \sqrt{\frac{3}{4}}$

$\implies 4 \cdot \frac{\sqrt{3}}{\sqrt{4}}$

$\implies {\cancel{4}}^{\textcolor{red}{2}} \cdot \frac{\sqrt{3}}{\cancel{2}}$

color(blue)(=> 2 sqrt3

Jul 10, 2018

$2 \sqrt{3}$

Explanation:

The key realization is that we can rewrite $\sqrt{\frac{3}{4}}$ as $\frac{\sqrt{3}}{\sqrt{4}}$. We now have

$4 \cdot \frac{\sqrt{3}}{\sqrt{4}}$

This simplifies to

$4 \cdot \frac{\sqrt{3}}{2}$

Cancelling out common factors

${\cancel{4}}^{2} \cdot \frac{\sqrt{3}}{\cancel{2}}$

$\implies 2 \sqrt{3}$

Hope this helps!