Divide 36√39/9√13. Provide an exact answer.

Answer 1

To simplify the expression \(\frac{36\sqrt{39}}{9\sqrt{13}}\), we can follow these steps:

1. Divide the numerical coefficients: \[ \frac{36}{9} = 4 \]

2. Keep the square roots as is for now: \[ \sqrt{39} / \sqrt{13} \]

3. Combine the square roots: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]

4. Combine the results: \[ 4 \cdot \sqrt{3} \]

Thus, the simplified expression is: \[ \boxed{4\sqrt{3}} \]