Which is equivalent to $\frac{\sqrt{5}}{\sqrt{3}}$ ? $\newline$ A. $\frac{\sqrt{5}}{3}$ $\newline$ B. $\frac{\sqrt{15}}{3}$ $\newline$ C. $\frac{5}{3}$ $\newline$ D. $\frac{5}{\sqrt{3}}$ $\newline$ E. $\frac{3}{\sqrt{15}}$

Full solution

Q. Which is equivalent to

\frac{\sqrt{5}}{\sqrt{3}}

\newline

\frac{\sqrt{5}}{3}

\newline

\frac{\sqrt{15}}{3}

\newline

\frac{5}{3}

\newline

\frac{5}{\sqrt{3}}

\newline

\frac{3}{\sqrt{15}}

Multiply and Simplify: We know that $(\sqrt{5})/(\sqrt{3})$ can be simplified by multiplying the numerator and denominator by $\sqrt{3}$ to get rid of the square root in the denominator. $\newline$ So, $(\sqrt{5})/(\sqrt{3}) \times (\sqrt{3})/(\sqrt{3}) = (\sqrt{5} \times \sqrt{3})/(\sqrt{3} \times \sqrt{3})$ .
Perform Multiplication: Now let's do the multiplication. $\newline$ $(\sqrt{5} \times \sqrt{3})/(\sqrt{3} \times \sqrt{3}) = (\sqrt{5 \times 3})/(3) = (\sqrt{15})/(3)$ .
Match with Options: Looking at the options, we see that $(\sqrt{15})/(3)$ matches option B. $\newline$ So, the equivalent expression is $(\sqrt{15})/(3)$ .