9√33/27√11
To simplify the expression 9√33/27√11, we can start by simplifying each radical separately.
Step 1: Simplify the numerator
√33 is the same as √(11 * 3). We can break it down further as √11 * √3.
So, the numerator 9√33 becomes 9√11 * √3.
Step 2: Simplify the denominator
√11 cannot be simplified any further.
Step 3: Simplify the whole expression
Now, the simplified expression becomes (9√11 * √3) / √11.
Since the denominator and numerator both have a square root of 11, we can cancel them out.
The final simplified expression is 9√3 / 1, which is just 9√3.
To simplify the expression 9√33/27√11, you can first simplify the numerator and the denominator separately.
For the numerator 9√33:
√33 can be simplified as √(3*11). Since 11 is a prime number, it cannot be simplified. Therefore, the expression becomes 9√(3*11) or 9√(33).
For the denominator 27√11:
27 can be simplified as 3*3*3 or 3^3.
The expression now becomes (3^3)√11 or 3√11*3√11*3√11.
Now, you can cancel out the common factors √11 in the numerator and denominator:
(9√(3*11))/(3√11*3√11*3√11) = (9)/(3√11*3√11)
Since 3*3 is 9, the final simplified expression is:
(9)/(9√11)
You can further simplify this expression by canceling out the common factor 9:
(9)/(9√11) = 1/√11
Therefore, the simplified expression is 1/√11.
To simplify the given expression, we need to rationalize the denominators.
Let's start by simplifying the fractions:
9√33 = √(9^2 * 33) = √(99)
27√11 = √(27^2 * 11) = √(729 * 11) = √(7992)
Now, let's rewrite the expression with rationalized denominators:
(√99) / (√7992)
To rationalize the denominator, we need to find the prime factors of 7992.
The prime factorization of 7992 is: 2^3 * 3 * 7^2 * 11
Now, let's rewrite the expression with the rationalized denominator:
(√99) / (√(2^3 * 3 * 7^2 * 11))
To rationalize the denominator, we can multiply both the numerator and denominator by the square root of the missing prime factors.
(√99 * √(2^3 * 3 * 7^2 * 11)) / (√(2^3 * 3 * 7^2 * 11) * √(2^3 * 3 * 7^2 * 11))
Simplifying the denominator:
(√99 * √(2^3 * 3 * 7^2 * 11)) / (√(2^3 * 3 * 7^2 * 11 * 2^3 * 3 * 7^2 * 11))
Now, the square root of a product is equal to the product of the square roots of the factors.
(√99 * √(2^3 * 3 * 7^2 * 11)) / (√(2^3) * √(3) * √(7^2) * √(11) * √(2^3) * √(3) * √(7^2) * √(11))
Simplifying further:
(√99 * √(2^3 * 3 * 7^2 * 11)) / (2 * √(3) * 7 * √(11) * 2 * √(3) * 7 * √(11))
Now we can cancel out the common factors in the numerator and denominator:
(√99 * √(2^3 * 3 * 7^2 * 11)) / (2 * 7 * 2 * √(3) * √(11) * √(3) * √(11))
Simplifying further:
(√99 * √(2^3 * 3 * 7^2 * 11)) / (4 * 7 * √(3) * √(11) * √(3) * √(11))
Now, multiplying the remaining square roots:
(√99 * √(2^3 * 3 * 7^2 * 11)) / (4 * 7 * √(3 * 11 * 3 * 11))
Simplifying the numerator:
√(99 * 2^3 * 3 * 7^2 * 11) / (4 * 7 * √(33))
Now, simplifying the expression:
√(5544) / (4 * 7 * √(33))
Lastly, the square root of 5544 is equal to 74.4271887.
Plugging in the values:
74.4271887 / (4 * 7 * √(33))
Now we can multiply the numbers in the denominator:
74.4271887 / (28 * √(33))
Simplifying further, the answer is:
2.65 / √(33)
So, the simplified form of the expression is 2.65 / √(33).