Chapter 11.8, Problem 29WE

To determine

To find: The simplification of the given expression.

Answer to Problem 29WE

The simplification of the given expression is $\frac{4\sqrt{14}-7\sqrt{2}}{2}$ .

Explanation of Solution

Given information:

The given expression is,

  $2\sqrt{\frac{7}{2}}+4\sqrt{\frac{7}{8}}-\frac{1}{2}\sqrt{98}$

The given expression is simplified as,

  $\begin{array}{c}2\sqrt{\frac{7}{2}}+4\sqrt{\frac{7}{8}}-\frac{1}{2}\sqrt{98}=2\frac{\sqrt{7}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}+4\frac{\sqrt{7}}{\sqrt{8}}\cdot \frac{\sqrt{8}}{\sqrt{8}}-\frac{1}{2}\sqrt{7\times 7\times 2}\\ =2\frac{\sqrt{14}}{2}+8\frac{\sqrt{14}}{8}-\frac{7}{2}\sqrt{2}\\ =2\sqrt{14}-\frac{7}{2}\sqrt{2}\\ =\frac{4\sqrt{14}-7\sqrt{2}}{2}\end{array}$

Thus, the simplification of the given expression is $\frac{4\sqrt{14}-7\sqrt{2}}{2}$ .