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

Answer 1

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

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

2. Simplify the square roots: \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

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

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

Answer 2

so the answer is 3√3?

Answer 3

I apologize for any confusion in my previous response. Let's clarify:

From our previous simplification, we found: \[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3}\sqrt{3} \]

This can also be written as: \[ \frac{\sqrt{3}}{3} \]

However, if you were looking for a different expression involving \(3\sqrt{3}\), that's not what we derived.

To state the simplification clearly:

\[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{\sqrt{3}}{3} \]

To represent it in a simplified fractional form involving a square root, it is best expressed as \(\frac{\sqrt{3}}{3}\).

If you meant something else or if you would like a different representation, please let me know!

Answer 4

so the answer is √3/3?

Answer 5

Yes, that's correct! The simplified form of the expression \(\frac{9\sqrt{33}}{27\sqrt{11}}\) is:

\[ \frac{\sqrt{3}}{3} \]

Thank you for your patience, and I apologize for any confusion earlier. If you have any more questions or need further clarification, feel free to ask!