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

Answer 1

To divide 9√33 by 27√11, we can simplify the expression as follows:

9√33 / 27√11 = (√(9) * √(33)) / (√(27) * √(11))

Now, we can simplify the square roots:

= (3√33) / (3√(11))

The 3's in the numerator and denominator cancel out, leaving us with:

= √(33) / √(11)

Since the denominator is the same as the numerator, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:

= (√(33) * √(11)) / (√(11) * √(11))

Simplifying further:

= √(33*11) / 11

= √(363) / 11

Therefore, the exact answer is √(363) / 11.