How do you solve (2sqrt3)/sqrt6?

Jun 19, 2018

$\frac{2 \sqrt{3}}{\sqrt{6}} = \textcolor{b l u e}{\sqrt{2}}$

Explanation:

(color(lime)2sqrt(3))/(color(magenta)sqrt(6)

$\textcolor{w h i t e}{\text{XXX}} = \frac{\textcolor{\lim e}{\sqrt{2} \cdot \sqrt{2}} \cdot \sqrt{3}}{\textcolor{m a \ge n t a}{\sqrt{2} \cdot \sqrt{3}}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{2}$

Jun 19, 2018

$\frac{2 \sqrt{3}}{\sqrt{6}} = \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$

Jun 19, 2018

$\sqrt{2}$

Explanation:

$\frac{2 \sqrt{3}}{\sqrt{6}}$

$\Rightarrow \frac{2 \sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}$

$\Rightarrow = \frac{2 \sqrt{18}}{\sqrt{36}}$

$\Rightarrow \frac{2 \cdot \sqrt{9} \cdot \sqrt{2}}{6}$

$\implies \frac{6 \sqrt{2}}{6}$

$\Rightarrow \sqrt{2}$.

Jun 24, 2018

$\implies \sqrt{2}$

Explanation:

$\sqrt{a} b = \sqrt{a} \cdot \sqrt{b}$, we can rewrite this expression as

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

Cancelling out common terms

(2cancel(sqrt3))/(sqrt2*cancel(sqrt3)

$\implies \frac{2}{\sqrt{2}}$

The convention is to not have an irrational number in the denominator, so let's multiply the top and bottom by $\sqrt{2}$.

$\frac{2 \cdot \sqrt{2}}{\sqrt{2}} ^ 2$

$\frac{2 \sqrt{2}}{2}$

$\frac{\cancel{2} \sqrt{2}}{\cancel{2}}$

$\implies \sqrt{2}$

Hope this helps!