divide 9√33 / 27√11 provide an exact answer
To simplify the expression 9√33 / 27√11, we can simplify the numerator and denominator separately.
First, let's simplify the numerator:
√33 can be written as 3√3
So, 9√33 becomes 9 * 3√3 which equals 27√3.
Now, let's simplify the denominator:
√11 cannot be simplified further.
So, the simplified expression becomes:
27√3 / 27√11
Since the denominator is the same as the numerator, the expression can be further simplified by canceling out the common factor.
27/27 equals 1.
Therefore, the exact answer is: 1√3 / √11.
To divide 9√33 by 27√11, we can simplify the expression by rationalizing the denominators.
First, let's rationalize the denominator of 27√11:
To do this, we multiply both the numerator and denominator by the conjugate of √11, which is -√11.
(27√11) * (-√11) = -297
Therefore, the denominator becomes -297.
Now let's simplify the numerator, 9√33, by rationalizing it as well:
To do this, we multiply both the numerator and denominator by the conjugate of √33, which is -√33.
(9√33) * (-√33) = -297
Therefore, the numerator becomes -297.
So, the division expression 9√33 / 27√11 simplifies to -297 / -297, which is equal to 1.
So, the exact answer is 1.
To divide 9√33 by 27√11, follow these steps:
Step 1: Simplify the square roots individually.
√33 cannot be simplified any further because it does not have any perfect square factors. Similarly, √11 cannot be simplified.
Step 2: Simplify the numbers outside the square roots.
9 and 27 have a common factor of 9. Divide both numbers by 9 to simplify them.
9 ÷ 9 = 1
27 ÷ 9 = 3
Step 3: Divide the numbers and square roots separately.
1 √33 / 3 √11
Step 4: Divide the numbers.
1 ÷ 3 = 1/3
Step 5: Divide the square roots.
√33 / √11
Step 6: Rationalize the denominator.
To rationalize the denominator, multiply both the numerator and denominator by √11.
(√33 / √11) * (√11 / √11) = (√363 / 11)
Step 7: Simplify the answer.
The final answer is (1/3) * (√363 / 11) or (√363 / 33).