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

Answer 1

To divide \( \frac{36\sqrt{39}}{9\sqrt{13}} \), you can simplify the fraction by dividing both the numerator and the denominator by any common factors. Here, both 36 and 9 can be divided by 9, and the radicals \( \sqrt{39} \) and \( \sqrt{13} \) can be simplified because \( 39 = 3 \times 13 \).

Let's simplify step by step:

\( \frac{36\sqrt{39}}{9\sqrt{13}} \)

Divide 36 by 9:

\( \frac{4\sqrt{39}}{\sqrt{13}} \)

Now, since \( 39 = 3 \times 13 \), we have:

\( \frac{4\sqrt{3\times13}}{\sqrt{13}} \)

We can simplify \( \sqrt{13} \) in the numerator and the denominator:

\( \frac{4\sqrt{3}\sqrt{13}}{\sqrt{13}} \)

Now, cancel out \( \sqrt{13} \) from the numerator and the denominator:

\( 4\sqrt{3} \)

So the exact answer is:

\( 4\sqrt{3} \)