Question

express in simplest form with a rational denominator.
\\(\dfrac{2}{\sqrt{27}}\\)

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{27}$. We know that $27 = 9\times3$, and $\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}$. So the expression becomes $\frac{2}{3\sqrt{3}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{3}$. So we have $\frac{2\times\sqrt{3}}{3\sqrt{3}\times\sqrt{3}}$.

Step3: Simplify the denominator

Simplify the denominator: $3\sqrt{3}\times\sqrt{3}=3\times(\sqrt{3})^2 = 3\times3 = 9$. The numerator is $2\sqrt{3}$. So the expression is now $\frac{2\sqrt{3}}{9}$.

Answer:

$\frac{2\sqrt{3}}{9}$