Divide 9√33 27√11 provide an exact answer

Answer 1

To divide 9√33 by 27√11, we will rationalize the denominators:

(9√33) / (27√11)

First, simplify the square root terms by finding the square roots of both the numerator and denominator:

√(33) = √(3 * 11) = √(3) * √(11) = √(11)√(3)
√(11)√(11) = 11

Now, substitute these expressions into the original division:

(9√(11)√(3)) / (27√(11))

Simplify the expression further by dividing the numerical coefficients:

9 / 27 = 1/3

Combine the square root terms:

(1/3)(√(11)√(3)) / √(11)

Since the square root of 11 appears in both the numerator and denominator, it cancels out:

(1/3)(√(3)) = √(3) / 3

Therefore, the exact answer is (√3)/3.