Question

express in simplest form with a rational denominator.
\\(\frac{6}{\sqrt{90}}\\)

Explanation:

Step1: Simplify the square root

$\sqrt{90} = \sqrt{9 \times 10} = 3\sqrt{10}$

Step2: Rewrite the original fraction

$\frac{6}{3\sqrt{10}} = \frac{2}{\sqrt{10}}$

Step3: Rationalize the denominator

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

Step4: Simplify the fraction

$\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}$

Answer:

$\frac{\sqrt{10}}{5}$