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

Answer 1

To divide the expression 9√33 ÷ 27√11, we can simplify the square roots first.

The square root of 33 can be simplified as follows:
√33 = √(3 x 11) = √3 x √11 = √3√11

The square root of 11 can be simplified as follows:
√11 = √(11) = √11

Now we can rewrite the expression as:
9√33 ÷ 27√11 = 9√3√11 ÷ 27√11

Next, we can cancel out the common factor in both the numerator and the denominator, which is √11:
(9√3√11) ÷ (27√11) = (9√3) ÷ (27)

Finally, we simplify the expression by dividing both the numerator and the denominator by their greatest common factor, which is 9:
(9√3) ÷ 27 = √3 ÷ 3

Therefore, the exact answer is √3 ÷ 3.