Question

Divide nine square root of 33 / 27 square root of 11 provide an exact answer

Answer 1

[AI-generated answer — Bot GPT 3.5]

To divide the expression (9√33) / (27√11), we can simplify it by rationalizing the denominators.

First, we will rationalize the denominator: √11.

Multiply both the numerator and the denominator by the conjugate of the denominator, which is √11:
(9√33 * √11) / (27√11 * √11)

Simplifying further:
(9√(33 * 11)) / (27 * √(11 * 11))
(9√(363)) / (27 * √(121))
(9√363) / (27 * 11)
√(363) / 33

Therefore, the exact answer is √(363) / 33.

Answer 2

[AI-generated answer — Explain Bot]

To divide expressions involving square roots, we can use the property of radicals that states √(A) / √(B) = √(A / B).

Given: 9√33 / 27√11

Step 1: Simplify the radicands (the numbers inside the square roots).
√33 can be simplified as √(3 * 11), which becomes √3√11.
√11 is already in its simplest form.

Step 2: Rewrite the expression using the simplified square roots.
9√33 / 27√11 = 9(√3√11) / 27√11

Step 3: Apply the square root division property and cancel out any common factors.
√3 / √11 = (√3 * (√11)) / (√11 * (√11))
= √(3 * 11) / (11)
= √33 / 11

Step 4: Simplify the expression.
9√33 / 27√11 = 9(√33 / 11) / 27
= (9 / 11)(√33 / 27)
= √33 / 27 * 9 / 11
= √33 / 297

Therefore, the exact answer to 9√33 / 27√11 is √33 / 297.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To divide (9√33) by (27√11) and provide an exact answer, you can simplify the square roots and rationalize the denominators.

1. First, simplify the square roots:
√33 = √(11 * 3) = √11 * √3
√11 cannot be further simplified, so we leave it as it is.
√3 cannot be simplified further, so we leave it as it is.

2. Rewrite the equation:
(9 * √11 * √3) / (27 * √11)

3. Next, simplify the numbers:
9 / 27 = 1/3

4. Rewrite the equation with the simplified numbers:
(1/3) * (√11 * √3) / √11

5. Rationalize the denominator by multiplying both the numerator and denominator by √11:
(1/3) * (√11 * √3 * √11) / (√11 * √11)

6. Simplify the equation:
(1/3) * (√11 * √3 * √11) / (√11 * √11)
= (1/3) * (√11 * √11 * √3) / (√11 * √11)
= (1/3) * (√11)^2 * √3 / (√11)^2
= (1/3) * 11 * √3 / 11
= √3 / 3

Therefore, the exact answer is √3 / 3.