divide 36√39/9√13 provide exact answer

Answer 1

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

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

2. Divide the square roots: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} \]

3. Calculate \( \frac{39}{13} \): \[ \frac{39}{13} = 3 \] So, \( \sqrt{\frac{39}{13}} = \sqrt{3} \).

4. Combine the results: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \sqrt{3} \]

Thus, the exact answer is: \[ 4\sqrt{3} \]