Question

simplify: $\frac{sqrt{2}}{2sqrt{3}}$

Explanation:

Step1: Rationalizar el denominador

Multiplicar numerador y denominador por $\sqrt{3}$
$\frac{\sqrt{2}}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{2} \times \sqrt{3}}{2 \times (\sqrt{3})^2}$

Step2: Simplificar las raíces y potencias

Usar $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ y $(\sqrt{a})^2 = a$
$\frac{\sqrt{6}}{2 \times 3} = \frac{\sqrt{6}}{6}$

Answer:

$\frac{\sqrt{6}}{6}$