Answer
$\frac{\sqrt {14}}{4}$
Work Step by Step
The simplification of the expression is only possible through rationalizing the denominator:
Step 1: $\sqrt \frac{7}{8}$
Step 2: $\frac{\sqrt 7}{\sqrt 8}$
Step 3: $\frac{\sqrt {7}}{\sqrt 8}\times\frac{\sqrt 8}{\sqrt 8}$
Step 4: $\frac{\sqrt 7\sqrt 8}{(\sqrt 8)^{2}}$
Step 5: $\frac{\sqrt {7\times8}}{8}$
Step 6: $\frac{\sqrt {7\times2\times4}}{8}$
Step 7: $\frac{\sqrt {7\times2}\times\sqrt 4}{8}$
Step 8: $\frac{\sqrt {7\times2}\times2}{8}$
Step 9: $\frac{2\sqrt {14}}{8}$
Step 10: $\frac{\sqrt {14}}{4}$
