Divided 9√33/27√11. Provide an exact answer.

Answer 1

To divide 9√33 by 27√11, we can simplify the expression.

First, we can simplify the numerator:

9√33 = √(9^2)√(11*3) = 3√(11*3) = 3√(33)

And we can simplify the denominator:

27√11 = √(3^3)√11 = 3√(11)

Now we can rewrite the expression:

(3√(33))/(3√(11)).

Since the denominators are the same, we can cancel them out:

(3√(33))/(3√(11)) = √(33)/√(11).

Now we can rationalize the denominator by multiplying the expression by the conjugate of the denominator:

(√(33)/√(11)) * (√(11)/√(11)) = (√(33)*√(11))/(√(11)*√(11)) = √(363)/11.

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