Question

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:
\[
\frac{36\sqrt{39}}{9\sqrt{13}} = 4\sqrt{3}
\]