To divide \( \frac{\sqrt{95}}{3\sqrt{5}} \), we start by simplifying the expression.
First, we can simplify \( \sqrt{95} \). Since \( 95 = 19 \times 5 \), we have:
\[ \sqrt{95} = \sqrt{19 \times 5} = \sqrt{19} \cdot \sqrt{5} \]
Now, substituting this back into the expression, we get:
\[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{19}\cdot\sqrt{5}}{3\sqrt{5}} \]
Next, we can simplify \( \frac{\sqrt{5}}{\sqrt{5}} \) which equals 1 (as long as \( \sqrt{5} \neq 0 \)):
\[ = \frac{\sqrt{19}}{3} \]
Thus, the exact answer is:
\[ \frac{\sqrt{19}}{3} \]
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