Divide 9√33 ÷ 27√11. Provide an exact answer.
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.
To divide 9√33 ÷ 27√11, we can simplify the expression by rationalizing the denominator.
Step 1: Simplify the expression by factoring the numbers under the square roots.
9√33 = 3√(3 × 11)
27√11 = 3 × 9√11
So, the expression becomes:
(3√(3 × 11)) ÷ (3 × 9√11)
Step 2: Simplify the expression further by canceling out common factors between the numerator and denominator.
(3√(3 × 11)) ÷ (3 × 9√11) = (√3 × √11) ÷ (3 × 3√11)
Step 3: Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
(√3 × √11) ÷ (3 × 3√11) = (√(3 × 11)) ÷ (3 × 3√11) × (√(3 × 11) / (√(3 × 11)))
= (√33) / (3 × 3 × √(3 × 11) × √(3 × 11))
= √33 / (3 × 3 × √(3 × 11)^2)
= √33 / (3 × 3 × √(9 × 33))
= √33 / (3 × 3 × 3√(3 × 11))
Therefore, the exact answer is √33 / (3 × 3 × 3√(3 × 11)).
To divide 9√33 by 27√11, we can simplify the expression by rationalizing the denominators first.
First, let's simplify the given expression:
9√33 ÷ 27√11
To rationalize the denominator (27√11), we need to multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of 27√11 is 27√11. By multiplying the numerator and denominator by it, we eliminate the square root from the denominator.
So, let's multiply both the numerator and denominator by 27√11:
(9√33 × 27√11) ÷ (27√11 × 27√11)
Simplifying the numerator:
9 × 27 × √(33 × 11) = 243√363
Simplifying the denominator:
27 × 27 × √(11 × 11) = 729√121 = 729 × 11 = 8019
Now, the expression becomes:
243√363 / 8019
To find an exact answer, we simplify the expression as much as possible.
The square root of 363 can be decomposed into square roots of smaller numbers:
√363 = √(121 × 3) = √121 × √3 = 11√3
Now our expression becomes:
243(11√3) / 8019
We can simplify further by dividing both the numerator and denominator by the greatest common divisor (GCD) of the terms:
243 and 8019 have a common factor of 9, so let's divide them by 9:
27(11√3) / 891
Now, we can simplify the expression to its simplest form:
11√3 / 33
Thus, the exact answer to 9√33 ÷ 27√11 is 11√3 / 33.