Divided 9√33/27√11. Provide an exact answer.
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.
To divide the expression (9√33)/(27√11), we can simplify the expression first.
Step 1: Simplify the numerator:
9√33 = 3√(3*11) = 3√3√11 = 3√3√11
Step 2: Simplify the denominator:
27√11 = 3*9√11 = 3*3√(11) = 3√(3*11) = 3√3√11 = 3√3√11
Step 3: Combine the numerator and denominator:
(3√3√11)/(3√3√11)
Step 4: Divide the numerator and denominator:
(3√3√11)/(3√3√11) = 1
The exact answer is 1.
To divide the expression 9√33 by 27√11 and provide an exact answer, we can simplify the expression by rationalizing the denominators.
First, let's simplify the expression 9√33:
√33 can be written as √(11 * 3), which can be further simplified as √11 * √3.
Thus, the expression becomes 9 * (√11 * √3).
Next, let's simplify the expression 27√11:
√11 cannot be simplified further.
Now, let's divide the two expressions:
(9 * (√11 * √3)) / 27√11.
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator, which is (√11 * √3). This will eliminate the radical in the denominator.
((9 * (√11 * √3)) / 27√11) * (√11 * √3) / (√11 * √3)
= ((9 * (√11 * √3)) * (√11 * √3)) / (27√11 * √11 * √3)
Simplifying further, we can multiply the numerators and denominators separately:
= (9 * 11 * 3) / (27 * 11 * √3 * √11)
Now, we can simplify the expression:
= (297) / (297√3)
The exact simplified answer is 1/√3, which can also be written as √3 / 3, after rationalizing the denominator.