Divide 9√33 by 27√11 . Provide an exact answer.
To divide 9√33 by 27√11, we can simplify the expression as follows:
9√33 / 27√11 = (√(9) * √(33)) / (√(27) * √(11))
Now, we can simplify the square roots:
= (3√33) / (3√(11))
The 3's in the numerator and denominator cancel out, leaving us with:
= √(33) / √(11)
Since the denominator is the same as the numerator, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
= (√(33) * √(11)) / (√(11) * √(11))
Simplifying further:
= √(33*11) / 11
= √(363) / 11
Therefore, the exact answer is √(363) / 11.
To divide 9√33 by 27√11, we can simplify the expression.
We start by simplifying the terms under the radical (√).
√33 can be written as √(11 × 3) = √11 × √3.
√11 cannot be simplified any further as it is not a perfect square, but we can simplify √3.
Now, let's substitute the simplified terms back into the original expression. We have:
(9√11 × √3) / (27√11).
Next, we can cancel out the common factors between the numerator and denominator, which is √11:
(9 × √3) / (27) = 9√3 / 27.
Now, we can simplify the expression by dividing both the numerator and denominator by 9:
(9÷9) × (√3 / 27) = 1 × (√3 / 27).
Therefore, the exact answer to the division of 9√33 by 27√11 is (√3 / 27).
To divide the expression 9√33 by 27√11, we can follow these steps:
Step 1: Simplify the radicals separately.
The square root of 33 cannot be simplified any further, so we leave it as is: 9√33.
The square root of 11 also cannot be simplified any further: 27√11.
Step 2: Divide the coefficients.
In this case, the 9 and 27 can be divided to get 1/3.
Step 3: Combine the radicals.
Since the radicals have the same term under the square root sign (33 and 11), we can combine them by division. The result is √(33/11).
Step 4: Simplify the square root.
The fraction 33/11 can be simplified to 3.
So, the exact answer is (1/3)√3.