Simplifying compound fraction: $\frac{3}{\sqrt{5}/5}$ I'm trying to simplify the following:
$$\frac{3}{\ \frac{\sqrt{5}}{5} \ }.$$
I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I multiply the numerator by the reciprocal of the denominator.
The problem is I interpreted that as:
$$\frac{3}{\ \frac{\sqrt{5}}{5} \ } \times \frac{5}{\sqrt{5}},$$
Which I believe is:
$$\frac{15}{\ \frac{5}{5} \ } = \frac{15}{1}.$$
What am I doing wrong?

You have the following fraction to simplify:
$$\begin{align} \frac{3}{\sqrt{5}/5} &=\frac{5\times 3}{\sqrt{5}} \\ &=\frac{15}{\sqrt{5}} \\ &=\sqrt{\bigg(\frac{15}{\sqrt{5}}\bigg)^2} \\ &=\sqrt{\frac{15^2}{\sqrt{5}^2}} \\ &=\sqrt{\frac{225}{5}} \\ &=\sqrt{45} \\ &= \sqrt{9\times 5} \\ &= \sqrt{9}\sqrt{5} \\ &= 3\sqrt{5} \\ \therefore \frac{15}{\sqrt{5}}\times \frac{5}{\sqrt{5}} &=\frac{15}{\sqrt{5}}\times \frac{\big(\frac{15}{\sqrt{5}}\big)}{3} \\ &=\frac{15}{\sqrt{5}}\times \frac{15}{\sqrt{5}}\times \frac{1}{3} \\ &=\bigg(\frac{15}{\sqrt{5}}\bigg)^2 \times \frac{1}{3} \\ &=45\times \frac{1}{3} \\ &=\frac{45}{3} \\ &=15 \end{align}$$
