Divide 9√33/27√11 Provide an exact answer.
To divide the expression 9√33/27√11, we can simplify it as follows:
Dividing the numbers: 9/27 simplifies to 1/3.
Dividing the square roots: √33/√11 simplifies to √(33/11).
Simplifying the fraction inside the square root: 33/11 simplifies to 3.
Therefore, √(33/11) is equal to √3.
Combining the results: 1/3 * √3 is equal to √3/3.
So the exact answer is √3/3.
To divide √33 by √11, we can simplify the radicals by finding the square roots of 33 and 11. The square root of 33 is √(11*3) which simplifies to √11 * √3.
Similarly, the square root of 11 is just √11.
Now we can divide (√33) / (√11) = (√11 * √3) / √11.
Since both radicals have the same denominator (√11), we can cancel them out and simplify the expression to √3.
So, the division 9√33 / 27√11 is equal to (9/27) * √3.
Simplifying further, 9/27 can be reduced to 1/3.
Therefore, the exact answer to the division 9√33 / 27√11 is (1/3) * √3.
To divide the expression (9√33) / (27√11) and provide an exact answer, we can follow these steps:
Step 1: Simplify the numerator and the denominator separately.
The numerator is 9√33.
The denominator is 27√11.
To simplify the square root of a number, we need to factorize it.
√33 can be written as √(11 * 3).
Thus, 9√33 = 9√(11 * 3).
Similarly, √11 can be left as it is: 27√11 = 27√11.
Step 2: Simplify the fraction.
Now we have (9√(11 * 3)) / (27√11).
We can simplify the fraction by dividing the numerator by the denominator:
(9√(11 * 3)) / (27√11) = (9 / 27) * (√(11 * 3) / √11).
Step 3: Further simplify the fraction.
The fraction (9 / 27) can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
The greatest common divisor of 9 and 27 is 9. Dividing both by 9 gives us 1/3.
Our expression becomes: (1/3) * (√(11 * 3) / √11).
Step 4: Simplify the square root expressions.
We can simplify √(11 * 3) as √33, and √11 remains the same.
Our expression becomes: (1/3) * (√33 / √11).
Step 5: Rationalize the denominator.
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of √11 is -√11.
Multiplying both the numerator and the denominator by -√11 gives us: (1/3) * (√33 / √11) * (-√11 / -√11).
Simplifying the expression, we have: (1/3) * (-√(33 * 11) / (-√11 * -√11)).
This simplifies to: (1/3) * (-√363 / 11).
Hence, the exact fraction form of (9√33) / (27√11) is (-√363 / 33).