Chapter 11.9, Problem 8WE

To determine

Simplify.

Answer to Problem 8WE

The simplified form of ${\left(8-\sqrt{6}\right)}^2$ is $70-16\sqrt{6}$ .

Explanation of Solution

Given information:

The expression ${\left(8-\sqrt{6}\right)}^2$ .

Formula used:

  ${\left(a-b\right)}^2=a^2+b^2-2ab$

  ${\left(8-\sqrt{6}\right)}^2$

As the expression resembles ${\left(a-b\right)}^2$ ,

we will use identity ${\left(a-b\right)}^2=a^2+b^2-2ab$

  $\begin{array}{l}{\left(8-\sqrt{6}\right)}^2\\ =8^2+{\left(\sqrt{6}\right)}^2-2\cdot 8\cdot \sqrt{6}\\ =64+6-16\sqrt{6}\\ =\boxed{70-16\sqrt{6}}\end{array}$

The simplified form of ${\left(8-\sqrt{6}\right)}^2$ is $70-16\sqrt{6}$ .