what does 36 square root of 39 divided by 9 square root of 13

Answer 1

To simplify the expression, we can simplify the square roots separately and then divide the results.

First, let's simplify √39:
We can split 39 into its prime factors: 39 = 3 * 13.
Therefore, √39 = √(3 * 13).
Since square roots can be split across multiplication, we can write: √(3 * 13) = √3 * √13.
So, √39 = √3 * √13.

Next, let's simplify √13:
Since 13 is a prime number, its square root cannot be simplified further.
So, √13 remains as √13.

Now, let's calculate the numerator:
36 * √39 = 36 * (√3 * √13) [substituting √39 as √3 * √13].
= 36 * √3 * √13.

And, let's calculate the denominator:
9 * √13 = 9 * √13.

Now, we can rewrite the expression as:
(36 * √3 * √13) / (9 * √13).

Since we have the same terms - √13 - in both numerator and denominator, we can cancel them out:
(36 * √3 * √13) / (9 * √13) = (36 * √3) / 9.

Simplifying further, we have:
(36 * √3) / 9 = (4 * 9 * √3) / 9 = 4 * √3.

Therefore, the expression 36√39 / 9√13 simplifies to 4√3.