Sqrt 95

Divide
3sqrt5. Provide an exact answer. (1 point)

3 answers

To simplify \(\frac{\sqrt{95}}{3\sqrt{5}}\), we start by simplifying the square roots.

We can rewrite \(\sqrt{95}\) in terms of \(\sqrt{5}\):

\[ \sqrt{95} = \sqrt{19 \cdot 5} = \sqrt{19} \cdot \sqrt{5} \]

Now, substituting this back into the original expression gives:

\[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{19} \cdot \sqrt{5}}{3\sqrt{5}} \]

Since \(\sqrt{5}\) in the numerator and the denominator can be canceled out (as long as \(\sqrt{5} \neq 0\)), we have:

\[ \frac{\sqrt{19} \cdot \sqrt{5}}{3\sqrt{5}} = \frac{\sqrt{19}}{3} \]

Thus, the exact answer is:

\[ \frac{\sqrt{19}}{3} \]

What’s the answer

The exact answer for \(\frac{\sqrt{95}}{3\sqrt{5}}\) is:

\[ \frac{\sqrt{19}}{3} \]