Divide 36√39 / 9√13 . Provide an exact answer. (1 point)
To divide these two terms, we can rationalize the denominators.
First, we rationalize the denominator of the first term, which is √13.
Multiplying the numerator and denominator of the first term by √13, we get:
36√39 * √13 / (9√13 * √13)
Simplifying the denominator, we have:
36√39 * √13 / (9 * 13)
Multiplying the denominators, we get:
36√39 * √13 / 117
Again, we rationalize the denominator, which is 117.
Multiplying the numerator and denominator by √117, we have:
(36√39 * √13 * √117) / (117 * √117)
Simplifying the numerator and denominator:
36 * √(39 * 13 * 117) / (117 * √(117 * 117))
The square root of 39 * 13 * 117 is √{3^2 * 13 * (3*13) * 117} = 3 * 13 * √(3 * 13) = 39√(3 * 13).
The square root of 117 * 117 = √{3^2 * 13^2} = 3 * 13 = 39.
Substituting these values, we have:
(36 * 39√(3 * 13)) / (117 * 39)
The 39 in the numerator and denominator can be canceled out:
36√(3 * 13) / 117
The √(3 * 13) is √39.
Therefore, the final answer is:
36√39 / 117√39 = 36 / 117 = 4/13.
So, the exact answer is 4/13.
are you sure?
I apologize for the mistake in my previous response. Let's solve the division correctly.
We are given:
(36√39) / (9√13)
To divide, we can simplify the expression by canceling out common factors between the numerator and denominator.
First, let's simplify the numerator and denominator:
36√39 can be simplified as (6√4)(6√39) = 6(2)(√3)(√13) = (12√3)(√13)
9√13 can be simplified as (3√4)(3√13) = 3(2)(√13) = (6√13)
Now let's divide the simplified terms:
(12√3)(√13) / (6√13)
Since the √13 term in both the numerator and denominator can be canceled out, we are left with:
12√3 / 6
Which simplifies further as:
(12/6)√3 = 2√3
Therefore, the exact answer is 2√3.
To divide 36√39 by 9√13, we can simplify it as follows:
Step 1: Divide the numerical parts: 36 ÷ 9 = 4.
Step 2: Divide the square root parts: √39 ÷ √13 = √(39/13) = √3.
Step 3: Combine the results: 4√3.
Therefore, 36√39 / 9√13 simplifies to 4√3.