To determine which choice is equivalent to the expression [tex]\(\frac{\sqrt{15}}{3 \sqrt{3}}\)[/tex], let's simplify it step-by-step:
1. Rewrite the numerator:
[tex]\[
\sqrt{15} \implies \sqrt{3 \times 5} = \sqrt{3} \times \sqrt{5}
\][/tex]
2. Substitute this back into the original expression:
[tex]\[
\frac{\sqrt{15}}{3 \sqrt{3}} = \frac{\sqrt{3} \times \sqrt{5}}{3 \sqrt{3}}
\][/tex]
3. Cancel out the common term [tex]\(\sqrt{3}\)[/tex] from the numerator and the denominator:
[tex]\[
\frac{\sqrt{3} \times \sqrt{5}}{3 \sqrt{3}} = \frac{\sqrt{5}}{3}
\][/tex]
Now we compare our simplified expression with the given choices:
A. [tex]\(\frac{\sqrt{5}}{3}\)[/tex]
B. [tex]\(\frac{\sqrt{5}}{\sqrt{3}}\)[/tex]
C. [tex]\(\frac{\sqrt{5}}{9}\)[/tex]
D. [tex]\(\sqrt{4}\)[/tex]
We see that the simplified expression [tex]\(\frac{\sqrt{5}}{3}\)[/tex] matches choice A.
Therefore, the correct choice is:
[tex]\[
\boxed{\frac{\sqrt{5}}{3}}
\][/tex]
