9√33 divided by 27√11
9√33 / by 27√11 = 9/27 * √33/√11 = 1/3 * √3 = 1/√3
To divide 9√33 by 27√11, we can simplify the expression by first simplifying the square root terms and then dividing the numbers separately.
Let's start by simplifying the square root terms:
√33 can be simplified as 3√3 (since √33 = √(11*3) = √11 * √3 = √11 * √(3) = √11√3 = 3√3)
√11 remains the same.
Now, we have:
9√33 = 9 * 3√3 = 27√3
27√11 remains the same.
The simplified expression is:
27√3 divided by 27√11
Since the square root terms are the same, we can cancel them out:
27√3/ 27√11 = (27/27) * (√3/√11) = 1 * (√3/√11) = √3/√11.
Therefore, the division of 9√33 by 27√11 simplifies to √3/√11.
To simplify this expression, we can first divide the numerator and denominator separately.
Numerator: 9√33
Denominator: 27√11
Dividing the numerator by 9:
9√33 / 9 = √33
Dividing the denominator by 27:
27√11 / 27 = √11
Therefore, the simplified expression is:
√33 / √11
Apologies for the mistake. Let's simplify the expression step by step:
9√33 / 27√11
To divide, we can simplify the numerator and denominator separately:
Numerator: 9√33 = 3√33 * 3
Denominator: 27√11 = 3√11 * 3
Now we can rewrite the expression as:
(3√33 * 3) / (3√11 * 3)
Cancel out the common factors of 3:
(√33 * 3) / (√11 * 3)
This simplifies to:
√33 / √11
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is √11:
(√33 / √11) * (√11 / √11)
This gives us:
(√33 * √11) / (√11 * √11)
Simplifying the numerator and denominator:
√(33*11) / √(11^2)
√363 / 11
Therefore, the simplified expression is:
√363 / 11