Chapter 11.8, Problem 37WE

To determine

To find: The simplification of the given expression.

Answer to Problem 37WE

The simplification of the given expression is $\frac{x\sqrt{a^2+b^2}}{ab}$ .

Explanation of Solution

Given information:

The given expression is,

  $\sqrt{\frac{x^2}{a^2}+\frac{x^2}{b^2}}$

The given expression is simplified as,

  $\begin{array}{c}\sqrt{\frac{x^2}{a^2}+\frac{x^2}{b^2}}=\sqrt{\frac{b^2{x}^2+a^2{x}^2}{a^2{b}^2}}\\ =\sqrt{\frac{\left(a^2+b^2\right)x^2}{a^2{b}^2}}\\ =\frac{x\sqrt{a^2+b^2}}{ab}\end{array}$

Thus, the simplification of the given expression is $\frac{x\sqrt{a^2+b^2}}{ab}$ .