Divide 36√39 / 9√13 . Provide an exact answer. (1 point)

Answer 1

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.

Answer 2

are you sure?

Answer 3

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.