divide 9√33 / 27√11
To divide the expression (9√33) by (27√11), we can simplify the expression by reducing the terms under the square roots and then dividing the coefficients separately.
First, let's simplify the expressions under the square roots:
√33 = √(3 * 11) = √3 * √11
√11 remains as it is.
Now we can rewrite the expression:
9√33 = 9√3 * √11
27√11 remains as it is.
Now we can divide the coefficients by each other:
9 / 27 = 1/3
Finally, we can combine the terms with square roots:
(1/3) * (√3 * √11) / √11
Since √11/√11 equals 1, we can cancel out the square roots:
(1/3) * √3 = √3 / 3
Therefore, the simplified expression is √3 / 3.
To divide 9√33 by 27√11, we can simplify the expression by rationalizing the denominators.
Step 1: Let's rationalize the denominator of 27√11. To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is √11.
9√33 / 27√11 * √11 / √11
= 9√363 / (27 * √11 * √11)
= 9√363 / (27 * √121)
= 9√363 / (27 * 11)
= 9√363 / 297
Step 2: Now, we can simplify the expression further if possible. We notice that 363 is divisible by 9, so we can simplify the numerator by dividing it by 9.
9√363 / 297 = √363 / 33
Therefore, the simplified expression of 9√33 / 27√11 is √363 / 33.
To divide the expression 9√33 by 27√11, we can simplify the terms first.
Let's simplify the square roots:
√33 cannot be simplified any further because 33 is not a perfect square.
√11 also cannot be simplified any further because it is not a perfect square.
Now, let's simplify the fractions:
9 divided by 27 is equal to 1/3.
So, the expression becomes:
(1/3) * (√33 / √11)
To divide two terms with the same base (√33 and √11), we can combine them into one term by dividing their coefficients:
(1/3) * (√33 / √11) = (1/3) * (√(33/11))
Now, we can simplify the expression further by dividing the numerator and denominator under the square root:
(1/3) * (√(33/11)) = (1/3) * (√3)
Therefore, the expression 9√33 / 27√11 simplifies to (1/3) * √3.