Chapter 11.10, Problem 3MRE

To determine

To find: The simplest form.

Answer to Problem 3MRE

The simplest form is $\left(\sqrt{11}-3\right)$ .

Explanation of Solution

Given:

The given equation is,

  $\frac{2}{3+\sqrt{11}}$

Calculation:

The equation is simplified as,

  $\begin{array}{c}\frac{2}{3+\sqrt{11}}=\frac{2}{3+\sqrt{11}}\times \frac{\left(3-\sqrt{11}\right)}{\left(3-\sqrt{11}\right)}\\ =\frac{2\left(3-\sqrt{11}\right)}{9-11}\\ =\frac{2\left(3-\sqrt{11}\right)}{-2}\\ =\left(\sqrt{11}-3\right)\end{array}$

Therefore, the simplest form is $\left(\sqrt{11}-3\right)$ .