what does 36 square root of 39 divided by 9 square root of 13
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.
To divide two square roots, we can simplify the expression by rationalizing the denominators.
First, let's simplify the square root of 39 and the square root of 13 separately:
- The square root of 39 can be factored as the square root of 3 multiplied by the square root of 13.
- The square root of 13 cannot be simplified further.
Now, let's rewrite the expression with the simplified square roots:
(36 * √(3 * 13)) / (9 * √13)
Next, we can cancel out the square root of 13 in both the numerator and denominator, as they are the same:
(36 * √(3 * 13)) / (9)
Simplifying further:
(36 * √39) / 9
Now, we can divide both the numerator and denominator by 9:
36 / 9 = 4
So, the final answer is 4 * √39.