Question

simplify the radical expression by rationalizing the denominator.

\\\sqrt{\frac{20}{55}}\\

give your answer in simplest form.

Explanation:

Simplify the fraction inside the radical

$$ \frac{20}{55} = \frac{4 \times 5}{11 \times 5} = \frac{4}{11} $$

Apply the quotient property of radicals

$$ \sqrt{\frac{4}{11}} = \frac{\sqrt{4}}{\sqrt{11}} = \frac{2}{\sqrt{11}} $$

Rationalize the denominator

$$ \frac{2}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{2\sqrt{11}}{11} = \frac{2}{11}\sqrt{11} $$

Answer:

Simplify the radical expression by rationalizing the denominator.

$$\sqrt{\frac{20}{55}}$$

Give your answer in simplest form.
<blank>\(\frac{2}{11}\sqrt{11}\)</blank>