divide 36 radical 39/9 radical 13. provide an exact answer

Answer 1

To simplify the expression \(\frac{36\sqrt{39}}{9\sqrt{13}}\), we can start by simplifying the coefficients and radicals separately.

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

2. Simplify the radicals: We need to simplify \(\frac{\sqrt{39}}{\sqrt{13}}\). We can combine the square roots: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} \]

   Now, divide \(39\) by \(13\): \[ \frac{39}{13} = 3 \] Therefore: \[ \sqrt{\frac{39}{13}} = \sqrt{3} \]

3. Combine the results: Now we can combine the simplified coefficient and the simplified radical: \[ 4 \cdot \sqrt{3} = 4\sqrt{3} \]

Putting all of this together, the exact simplified answer is: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4\sqrt{3} \]