Divide 9√33/27√11
To divide 9√33 by 27√11, we can follow these steps:
Step 1: Simplify the denominators
The square roots in the denominators cannot be simplified any further. However, we can simplify the numbers outside the square roots by finding their greatest common divisor (GCD). The GCD of 9 and 27 is 9, and the GCD of 33 and 11 is 11. Therefore, we have:
9√33/27√11 = (√33 / √11) * (9/27) = (√3 * √11) / (√11) * (1/3)
Step 2: Cancel out the square roots
In the numerator, we have both √3 and √11. Since they both have the same square root (√11), we can cancel them out, resulting in:
(1/3) * √3
Therefore, 9√33 / 27√11 simplifies to (1/3) * √3
To divide the given expression, we can simplify the square roots and the numbers separately.
First, let's simplify the square roots:
√33 = √(9 x 3) = √9 x √3 = 3√3
√11 = √(9 x 2/3 x 3) = √9 x √(2/3) x √3 = 3√(2/3) x √3 = 3√2
Now, let's simplify the numbers:
9/27 = 1/3
Putting it all together, we have (9√33)/(27√11) = (1/3)(3√3)/(3√2)
Now, we can cancel out the 3's:
(1/3)(√3)/(√2)
Therefore, the answer is (1/3)(√3/√2).
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator:
(1/3)(√3/√2) x (√2/√2)
= (1/3)(√6/2)
= √6/6
So, the final answer is √6/6.
To divide the given expression 9√33 / 27√11, we can simplify it by rationalizing the denominators.
Step 1: Simplify the numerator.
9√33 = √(9^2 * 11) = 3√(11)
Step 2: Simplify the denominator.
27√11 = √(27^2 * 11) = 3 * 9√(11)
Now we have the expression in the form (3√(11)) / (3 * 9√(11)).
Step 3: Cancel out the common factors.
The 3's in the numerator and denominator can be canceled out, leaving us with
√(11) / (9√(11)).
Step 4: Rationalize the denominator.
To rationalize the denominator, we multiply both the numerator and denominator by √(11), which eliminates the square root in the denominator.
(√(11) * √(11)) / (9√(11) * √(11)) = 11 / (9 * 11) = 11 / 99.
Therefore, the simplified result of 9√33 / 27√11 is 11 / 99.
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To divide 9√33 by 27√11, we can follow these steps:
Step 1: Simplify the denominators
The square roots in the denominators cannot be simplified any further. However, we can simplify the numbers outside the square roots by finding their greatest common divisor (GCD). The GCD of 9 and 27 is 9, and the GCD of 33 and 11 is 11. Therefore, we have:
9√33/27√11 = (√33 / √11) * (9/27) = (√3 * √11) / (√11) * (1/3)
Step 2: Cancel out the square roots
In the numerator, we have both √3 and √11. Since they both have the same square root (√11), we can cancel them out, resulting in:
(1/3) * √3
Therefore, 9√33 / 27√11 simplifies to (1/3) * √3.