Question

9 rationalize the radicals below. ensure your final answer is as simplified as possible:
\\(\frac{\sqrt{5}}{\sqrt{3}} = \square\\)

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{3}$

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{3}$. So we have $\frac{\sqrt{5} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$.

Step2: Simplify the expression

We know that $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ and $\sqrt{a}\times\sqrt{a} = a$ (for non - negative real numbers $a$ and $b$). So $\sqrt{5}\times\sqrt{3}=\sqrt{15}$ and $\sqrt{3}\times\sqrt{3}=3$. Then the expression becomes $\frac{\sqrt{15}}{3}$.

Answer:

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