Question

rationalize the denominator.

\\\frac{\sqrt{6}}{\sqrt{11}}\\

\\\frac{\sqrt{6}}{\sqrt{11}} = \text{ } (\text{simplify your answer.})\\

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Multiply numerator and denominator

To eliminate the radical in the denominator, multiply both the numerator and the denominator by \(\sqrt{11}\):

$$ \frac{\sqrt{6}}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}} $$

Step 2: Simplify the expression

Apply the product property of radicals, \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\):

$$ \frac{\sqrt{6 \cdot 11}}{\sqrt{11 \cdot 11}} = \frac{\sqrt{66}}{11} $$

Answer:

$$ \frac{\sqrt{66}}{11} $$