Divide 9√33 27√11 provide an exact answer
To divide 9√33 by 27√11, we will rationalize the denominators:
(9√33) / (27√11)
First, simplify the square root terms by finding the square roots of both the numerator and denominator:
√(33) = √(3 * 11) = √(3) * √(11) = √(11)√(3)
√(11)√(11) = 11
Now, substitute these expressions into the original division:
(9√(11)√(3)) / (27√(11))
Simplify the expression further by dividing the numerical coefficients:
9 / 27 = 1/3
Combine the square root terms:
(1/3)(√(11)√(3)) / √(11)
Since the square root of 11 appears in both the numerator and denominator, it cancels out:
(1/3)(√(3)) = √(3) / 3
Therefore, the exact answer is (√3)/3.
To divide 9√33 by 27√11 and get an exact answer, we can simplify the expression first.
Let's break down each term:
9√33 = 3√33 * 3
27√11 = 3√11 * 9
Now we can rewrite the division expression as:
(3√33 * 3) / (3√11 * 9)
Next, we can simplify further by canceling out common factors:
(3/3) * (√33/√11) * (3/9)
Notice that 3/3 simplifies to 1 and 3/9 simplifies to 1/3:
1 * (√33/√11) * (1/3)
We can combine these factors:
√33/√11 * 1/3
Now, to handle the square roots in the numerator and denominator, we can rationalize the denominator (eliminate the square root). To do this, we multiply the numerator and denominator by the conjugate of the denominator.
So, we multiply (√33/√11) by (√11/√11):
√33/√11 * √11/√11 = √(33 * 11) / 11
Simplifying further:
√(33 * 11) / 11 = √363 / 11
Therefore, the exact answer to the division of 9√33 by 27√11 is √363/11.
To divide the expression 9√33 by 27√11, follow these steps:
Step 1: Simplify the given expression.
- Divide both the numerator and denominator by the GCD (Greatest Common Divisor) of 9 and 27, which is 9.
- Divide both the numerator and denominator by the GCD of √33 and √11, which is √33.
This gives us:
(9/9) * (√33/√33) / (27/9) * (√11/√33)
Step 2: Simplify the expression further.
- The term (9/9) simplifies to 1, and (√33/√33) simplifies to 1, so we can remove them from the expression.
This leaves us with:
1 / (27/9) * (√11/√33)
Step 3: Divide the numerator and denominator separately.
- Divide the numerator 1 by the denominator (27/9).
- Divide the terms √11 and √33 separately.
The expression becomes:
1 / (27/9) * (√11/√33) = 1 * (9/27) * (√11/√33)
= 9/27 * (√11/√33)
Step 4: Simplify the expression.
- Reduce the fraction 9/27 by dividing both the numerator and denominator by the GCD of 9 and 27, which is 9.
This gives us:
(9/9) * (√11/√33) / (27/9)
= 1 * (√11/√33) / (27/9)
Simplifying the denominator further, we get:
(√11/√33) / (3/1)
Now, dividing the two fractions is equivalent to multiplying the first fraction by the reciprocal of the second fraction.
So, the final answer is:
(√11/√33) * (1/3)
Thus, the exact answer to divide 9√33 by 27√11 is (√11/√33) * (1/3).