Question

exercises
simplify the quotient.

1. \\(\frac{\sqrt{5}}{\sqrt{10}}\\)

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{5}}{\sqrt{10}} = \sqrt{\frac{5}{10}}$

Step2: Simplify the fraction inside

$\sqrt{\frac{5}{10}} = \sqrt{\frac{1}{2}}$

Step3: Rationalize the denominator

$\sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{2}}{2}$

Answer:

$\frac{\sqrt{2}}{2}$