Step-by-step explanation:
To simplify \( \frac{3}{3\sqrt{5}} \), you can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of \( 3\sqrt{5} \) is \( 3\sqrt{5} \).
So, multiplying both the numerator and denominator by \( 3\sqrt{5} \), we get:
\[
\frac{3}{3\sqrt{5}} \times \frac{3\sqrt{5}}{3\sqrt{5}} = \frac{3 \times 3\sqrt{5}}{3 \times 3\sqrt{5}} = \frac{9\sqrt{5}}{9 \times 5} = \frac{9\sqrt{5}}{45}
\]
Finally, we can simplify further by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
\[
\frac{9\sqrt{5}}{45} = \frac{\cancel{9}\sqrt{5}}{\cancel{9} \times 5} = \frac{\sqrt{5}}{5}
\]
So, \( \frac{3}{3\sqrt{5}} \) simplifies to \( \frac{\sqrt{5}}{5} \).
