divide 9√33 by 27√11
To simplify the expression (9√33) / (27√11), we can multiply the numerator and denominator by √11 to rationalize the denominator:
(9√33 * √11) / (27√11 * √11)
Simplifying further:
(9 * √(33 * 11)) / (27 * √(11 * 11))
Multiplying under the square roots:
(9 * √363) / (27 * √121)
Now simplifying the square roots separately:
√363 = √(121 * 3) = √121 * √3 = 11√3
√121 = 11
Substituting these values back into the expression:
(9 * 11√3) / (27 * 11)
Simplifying:
(99√3) / 297
Now, we can divide 99 by 297, which simplifies to 1/3:
1/3 * √3
Therefore, (9√33) / (27√11) simplifies to √3/3.
To divide 9√33 by 27√11, you can simplify the expression using the rules of radical operations and then perform the division.
Here's how to do it step by step:
Step 1: Simplify the radicals individually.
√33 can be simplified as √(11 * 3), which gives us √11 * √3.
√11 cannot be simplified further.
√3 cannot be simplified further.
√11 can be simplified as 1√11, as the square root of any number can also be written with an exponent of 1.
√3 cannot be simplified further.
Step 2: Combine the simplified radicals.
9√33 becomes 9 * √11 * √3.
27√11 becomes 27 * 1√11.
Step 3: Perform the division.
(9 * √11 * √3) / (27 * 1√11)
To divide fractions, you multiply by the reciprocal of the second fraction.
In this case, the reciprocal of 27 * 1√11 is (1 / (27 * 1√11)).
Multiplying the numerator and denominator by the reciprocal, we get:
(9 * √11 * √3) / (27 * 1√11) * (1 / (27 * 1√11))
Simplifying further, we have:
(9 * 1√11 * √3) / (27 * 27 * 1√11 * √11)
The √11 in the numerator cancels out with the √11 in the denominator:
(9 * 1 * √3) / (27 * 27 * 1)
Simplifying further, we get:
9√3 / 729
So, the simplified result of dividing 9√33 by 27√11 is 9√3 / 729.
To divide 9√33 by 27√11, we start by simplifying the radicals:
√33 can be simplified as 3√11, and √11 can't be simplified further.
Therefore, we rewrite the expression as (9 * 3√11) / (27 * √11).
Now, we can cancel out the common factor of 3 in the numerator and 27 in the denominator:
(3 * 3√11) / (9 * √11).
This further simplifies to (√11) / 3.
So, the result of dividing 9√33 by 27√11 is (√11) / 3.