Divide nine square root of 33/27 square root of 11 provide the exact answer

Answer 1

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

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

2. Combine the square roots: \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \] (since \( \frac{33}{11} = 3 \))

3. Combine the results: \[ \frac{1}{3} \sqrt{3} \]

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