Divide 9√33 / 27√11 . Provide an exact answer.

Answer 1

To divide \( \frac{9\sqrt{33}}{27\sqrt{11}} \), we can simplify this expression step-by-step.

1. Simplify the coefficients: \[ \frac{9}{27} = \frac{1}{3} \]

2. Write the square roots under a single square root: \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

3. Combine the results: \[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3} \cdot \sqrt{3} = \frac{\sqrt{3}}{3} \]

Thus, the exact answer is: \[ \frac{\sqrt{3}}{3} \]