divide 9√33 / 27√11 provide an exact answer
To divide the expression 9√33 by 27√11, you can simplify it by dividing the numbers outside the square roots and the numbers inside the square roots separately.
First, simplify the numbers outside the square roots: 9 divided by 27 equals 1/3.
Then, simplify the numbers inside the square roots: √33 divided by √11 is equal to √(33/11), which simplifies to √3.
Now, combine the two simplified expressions: (1/3) * √3.
Thus, the exact answer of 9√33 / 27√11 is (1/3) * √3.
To divide two terms that have square roots, we need to rationalize the denominators. In this case, we need to rationalize the denominators of 9√33 and 27√11.
Step 1: Rationalize the first denominator (27√11):
To rationalize 27√11, we need to multiply both the numerator and the denominator by the conjugate of the denominator, which is √11.
9√33 / (27√11) * (√11 / √11)
= (9√33 * √11) / (27 * 11)
= 9√(33 * 11) / 297
Step 2: Simplify the expression:
Now, we can simplify the expression by dividing the numbers and combining the square roots.
9√(33 * 11) / 297
= 9√363 / 297
This is the simplified form of the division.
However, if you want to express the answer in exact rational form, you should check if the square root can be further simplified by checking if it has any perfect square factors.
The prime factorization of 363 is:
363 = 3 * 121 = 3 * 11 * 11
Since there are no perfect square factors, we cannot simplify the square root any further.
Therefore, the exact answer is 9√363 / 297.
To divide 9√33 by 27√11 and provide an exact answer, we can simplify the expression as follows:
Step 1: Rewrite the expression using rationalizing denominators:
9√33 / 27√11 = (9/27) * (√33/√11)
Step 2: Simplify the fraction:
9/27 reduces to 1/3, so the expression becomes:
(1/3) * (√33/√11)
Step 3: Combine the terms under the square root:
To simplify, we can multiply the square roots together:
(1/3) * (√(33 * 11) / (√11)
Step 4: Simplify the resulting square root:
The square root of (33 * 11) is √363.
Final Answer: Therefore, the simplified expression is
(1/3) * (√363/√11)