9√33÷27√11
To simplify the expression 9√33 ÷ 27√11, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of 27√11 is -27√11, so we multiply both the numerator and denominator by -27√11:
(9√33 * -27√11) / (27√11 * -27√11)
Simplifying further:
-243√(33*11) / 729(11)
-243√(363) / 7992
Therefore, 9√33 ÷ 27√11 simplifies to -243√363 / 7992.
To simplify the expression 9√33 ÷ 27√11, we can start by simplifying the individual radicals (square roots) and then perform the division.
Step 1: Simplify the individual radicals
√33 cannot be simplified any further because it does not have any perfect square factors. Similarly, √11 is already in its simplest form.
Step 2: Simplify the division
To divide the two radicals, divide the coefficients (numbers outside the radicals) and the radicands (numbers inside the radicals) separately:
9/27 = 1/3 and √33/√11 = √(33/11) = √3
Putting it all together, the expression simplifies to:
(1/3) √3
Therefore, the simplified form of 9√33 ÷ 27√11 is (1/3) √3.
To simplify the expression 9√33÷27√11, we can follow these steps:
Step 1: Simplify the numerator (9√33).
We can break down 33 into its prime factors: 33 = 11 * 3.
Therefore, 9√33 becomes 9√(11 * 3).
Step 2: Simplify the denominator (27√11).
We can break down 27 into its prime factors: 27 = 3 * 3 * 3.
Therefore, 27√11 becomes 3√(11 * 3).
Step 3: Combine the simplified numerator and denominator.
The simplified expression becomes: (9√(11 * 3)) / (3√(11 * 3)).
Step 4: Simplify the expression further.
Since the numerator and denominator have the same term, which is √(11 * 3), we can simplify it by canceling them out.
The simplified expression becomes: 9 / 3.
Step 5: Simplify the resulting fraction.
9 divided by 3 equals 3.
Therefore, the final simplified expression is 3.