Chapter 11.8, Problem 35WE

To determine

To find: The simplification of the given expression.

Answer to Problem 35WE

The simplification of the given expression is $\frac{x\sqrt{41}}{20}$ .

Explanation of Solution

Given information:

The given expression is,

  $\sqrt{\frac{x^2}{16}+\frac{x^2}{25}}$

The given expression is simplified as,

  $\begin{array}{c}\sqrt{\frac{x^2}{16}+\frac{x^2}{25}}=\sqrt{\frac{25x^2+16x^2}{400}}\\ =\sqrt{\frac{41x^2}{400}}\\ =\frac{x\sqrt{41}}{20}\end{array}$

Thus, the simplification of the given expression is $\frac{x\sqrt{41}}{20}$ .