Question

rationalize the denominator and simplify.\\(\frac{sqrt{3}}{sqrt{5}}\\)

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $\sqrt{5}$:
$\frac{\sqrt{3}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{3} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}}$

Step2: Simplify numerator and denominator

Use $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ and $\sqrt{a} \times \sqrt{a} = a$:
$\frac{\sqrt{15}}{5}$

Answer:

$\frac{\sqrt{15}}{5}$