Question

express in simplest form with a rational denominator.\\(\dfrac{1}{\sqrt{18}}\\)

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{18}$. We know that $18 = 9\times2$, and $\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$. So, $\frac{1}{\sqrt{18}}=\frac{1}{3\sqrt{2}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$. So we have $\frac{1\times\sqrt{2}}{3\sqrt{2}\times\sqrt{2}}$.

Step3: Simplify the expression

Simplify the denominator: $\sqrt{2}\times\sqrt{2} = 2$. So the expression becomes $\frac{\sqrt{2}}{3\times2}=\frac{\sqrt{2}}{6}$.

Answer:

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