Question

which expression is the simplest form of \\(\frac{5}{\sqrt{8}}\\)?\
a \\(5\sqrt{8}\\)\
c \\(\frac{5\sqrt{2}}{4}\\)\
b \\(10\sqrt{2}\\)\
d \\(\frac{5\sqrt{8}}{8}\\)

Explanation:

Step1: Simplify the denominator

$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

Step2: Rewrite the original expression

$\frac{5}{\sqrt{8}} = \frac{5}{2\sqrt{2}}$

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{2}$:
$\frac{5 \times \sqrt{2}}{2\sqrt{2} \times \sqrt{2}} = \frac{5\sqrt{2}}{2 \times 2} = \frac{5\sqrt{2}}{4}$

Answer:

C. $\frac{5\sqrt{2}}{4}$