9√33 ÷ 27√11

Answer 1

To simplify the expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \), you can follow these steps:

1. Simplify the coefficients: Divide the numbers outside the square roots. \[ \frac{9}{27} = \frac{1}{3} \]

2. Simplify the square roots: Use the property of division under the square root. \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

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

Thus, the simplified form of \( \frac{9\sqrt{33}}{27\sqrt{11}} \) is: \[ \frac{\sqrt{3}}{3} \]