Question

express in simplest form with a rational denominator. $\frac{2}{sqrt{90}}$

Explanation:

Step1: Simplify the denominator

$\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$
So the fraction becomes $\frac{2}{3\sqrt{10}}$.

Step2: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{10}$:
$\frac{2\times\sqrt{10}}{3\sqrt{10}\times\sqrt{10}}=\frac{2\sqrt{10}}{3\times10}$

Step3: Simplify the fraction

$\frac{2\sqrt{10}}{30}=\frac{\sqrt{10}}{15}$

Answer:

$\frac{\sqrt{10}}{15}$