Question

exercises
simplify the quotient.

1. \\(\frac{4}{\sqrt{8}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{8}$:
$\frac{4}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}} = \frac{4\sqrt{8}}{8}$

Step2: Simplify the fraction

Reduce $\frac{4}{8}$ to $\frac{1}{2}$:
$\frac{4\sqrt{8}}{8} = \frac{\sqrt{8}}{2}$

Step3: Simplify the square root

Rewrite $\sqrt{8}$ as $\sqrt{4 \times 2} = 2\sqrt{2}$:
$\frac{\sqrt{8}}{2} = \frac{2\sqrt{2}}{2}$

Step4: Cancel common factors

Cancel the 2 in numerator and denominator:
$\frac{2\sqrt{2}}{2} = \sqrt{2}$

Answer:

$\sqrt{2}$