Divide 9√33 divided by 27√11 Provide an exact answer.
To divide 9√33 by 27√11, we can simplify the expression as follows:
9√33 divided by 27√11 = (9/27) * (√33/√11)
The simplified fraction (9/27) reduces to 1/3:
(1/3) * (√33/√11)
We can combine the square root terms by simplifying their multiplication:
(1/3) * (√(33/11))
Since the square root of 33 divided by the square root of 11 cannot be simplified any further, the final exact answer is:
(1/3) * (√(33/11))
To divide 9√33 by 27√11, you can follow these steps:
Step 1: Simplify the numerator and denominator separately.
9√33 can be simplified as 3√33, while 27√11 simplifies to 3√11.
Step 2: Divide the simplified numerator by the denominator.
3√33 ÷ 3√11 can be simplified further by trying to remove any common factors. However, since there are no common factors between 33 and 11, we cannot simplify it any further.
Step 3: Write down the simplified expression as the final answer.
Therefore, the exact division of 9√33 divided by 27√11 is:
(3√33) / (3√11)
To divide two numbers in radical form, we can simplify the radical expressions and then divide the coefficients outside the radicals.
Let's first simplify the radicals:
√33 = √(11 * 3) = √11 * √3 = √11√3
√11 cannot be simplified any further.
Now let's simplify the other radical:
√11 = √(11 * 1) = √11 * √1 = √11
Now we can divide the coefficients outside the radicals:
9/27 = 1/3
Putting it all together:
(9√33) / (27√11) = (1/3)(√11√3) / (√11) = (1/3)(√3)
So the exact answer is 1/3 * √3.