To divide \(\sqrt{95}\) by \(3\sqrt{5}\), you start by writing the expression as:
\[ \frac{\sqrt{95}}{3\sqrt{5}} \]
Next, we can simplify the expression. We can combine the square roots in the numerator:
\[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{95}}{\sqrt{5}} \cdot \frac{1}{3} \]
Now, simplify \(\frac{\sqrt{95}}{\sqrt{5}}\):
\[ \frac{\sqrt{95}}{\sqrt{5}} = \sqrt{\frac{95}{5}} = \sqrt{19} \]
Now, substituting back, we have:
\[ \frac{\sqrt{19}}{3} \]
Thus, the exact answer is:
\[ \frac{\sqrt{19}}{3} \]