divide 9√33 by 27√11. Provide an exact answer
To divide 9√33 by 27√11, we can simplify each radical separately.
First, let's simplify 9√33:
9√33 = √(9*33) = √297 = √(3*99) = √(3^2 * 11) = 3√11
Now, let's simplify 27√11:
27√11 = √(27*11) = √297 = √(3^3 * 11) = 3√(3*11) = 3√(33)
Therefore, 9√33 divided by 27√11 is equal to (3√11) / (3√33).
By dividing the coefficients (3/3) and dividing the radicands (√11 / √33), we get the final exact answer:
(3 / 3) * (√11 / √33) = 1 * (√11 / √33) = √11 / √33
To divide 9√33 by 27√11, we can simplify the expression as follows:
First, let's simplify the square roots:
√33 = √(11 * 3) = √11 * √3
√11 is already in its simplest form.
Now, let's divide the coefficients and simplify the expression further:
9/27 = 1/3
Putting everything together, we get:
(1/3) * (√11 * √3) / √11
Since we have a common square root term in the numerator and denominator (√11), we can cancel it out:
1/3 * √3
Therefore, 9√33 divided by 27√11 simplifies to:
1/3 * √3
To divide 9√33 by 27√11 and provide an exact answer, we'll follow these steps:
1. Recall the property of radicals: √a / √b = √(a/b). We can use this property to simplify the division of radicals.
2. Begin by dividing the coefficients (the numbers outside the square roots) of 9 and 27: 9 / 27 = 1/3.
3. Next, divide the numbers inside the square roots: √33 / √11 = √(33/11) = √3.
4. Combine the results of step 2 and step 3: (1/3) * √3.
5. The exact answer is (1/3) * √3.
In simplified form, the division of 9√33 by 27√11 is (1/3) * √3.