what is the simplest form of $\frac{2sqrt{3}}{sqrt{6}}$?\n$sqrt{2}$\n$sqrt{3}$\n$3sqrt{2}$\n$2sqrt{3}$\ndone

Explanation:

Step1: Rationalize the denominator

Multiply the fraction $\frac{2\sqrt{3}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$. So we get $\frac{2\sqrt{3}\times\sqrt{6}}{\sqrt{6}\times\sqrt{6}}$.

Step2: Simplify the numerator and denominator

For the numerator, $\sqrt{3}\times\sqrt{6}=\sqrt{3\times6}=\sqrt{18}=\sqrt{9\times2} = 3\sqrt{2}$, then $2\sqrt{3}\times\sqrt{6}=2\times3\sqrt{2}=6\sqrt{2}$. The denominator $\sqrt{6}\times\sqrt{6}=6$. So the fraction becomes $\frac{6\sqrt{2}}{6}$.

Step3: Cancel out the common factor

Cancel out the common factor 6 in the fraction $\frac{6\sqrt{2}}{6}$, we get $\sqrt{2}$.

Answer:

$\sqrt{2}$