Question

simplify the following radical expression by rationalizing the denominator.
\\(\frac{\sqrt{6}}{\sqrt{22}}\\)
answer

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{22}$:
$\frac{\sqrt{6}}{\sqrt{22}} \times \frac{\sqrt{22}}{\sqrt{22}} = \frac{\sqrt{6 \times 22}}{22}$

Step2: Simplify the radical

Calculate the product inside the square root and factor:
$\frac{\sqrt{132}}{22} = \frac{\sqrt{4 \times 33}}{22} = \frac{2\sqrt{33}}{22}$

Step3: Reduce the fraction

Cancel the common factor of 2:
$\frac{2\sqrt{33}}{22} = \frac{\sqrt{33}}{11}$

Answer:

$\frac{\sqrt{33}}{11}$