Question

to rationalize a fraction means to remove the radical from the denominator.
to rationalize \\(\frac{3}{\sqrt{5}}\\) multiply by the fraction \\(\frac{\sqrt{5}}{\sqrt{5}}\\) which is equivalent to 1. multiplying by 1 does not change the value of the fraction.
rationalize \\(\frac{3}{\sqrt{5}}\\)
\\(\bigcirc\\ 3\sqrt{5}\\)
\\(\bigcirc\\ 3\\)
\\(\bigcirc\\ \frac{3}{5}\\)
\\(\bigcirc\\ \frac{3\sqrt{5}}{5}\\)

Explanation:

Step1: Multiply by conjugate

Multiply \(\frac{3}{\sqrt{5}}\) by \(\frac{\sqrt{5}}{\sqrt{5}}\) (since \(\frac{\sqrt{5}}{\sqrt{5}} = 1\), the value remains).
\(\frac{3}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{3 \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}}\)

Step2: Simplify denominator

Simplify \(\sqrt{5} \times \sqrt{5}\) using \(\sqrt{a} \times \sqrt{a} = a\).
\(\sqrt{5} \times \sqrt{5} = 5\), so the fraction becomes \(\frac{3\sqrt{5}}{5}\).

Answer:

D. \(\frac{3\sqrt{5}}{5}\) (assuming the last option is D; if options are labeled as per the image, the correct one is the last option: \(\boldsymbol{\frac{3\sqrt{5}}{5}}\))