Chapter 11.9, Problem 7WE

To determine

Simplify.

Answer to Problem 7WE

The simplified form of ${\left(2+\sqrt{7}\right)}^2$ is $11+4\sqrt{7}$ .

Explanation of Solution

Given information:

The expression ${\left(2+\sqrt{7}\right)}^2$ .

Formula used:

  ${\left(a+b\right)}^2=a^2+b^2+2ab$

  ${\left(2+\sqrt{7}\right)}^2$

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

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

  $\begin{array}{l}{\left(2+\sqrt{7}\right)}^2\\ =2^2+{\left(\sqrt{7}\right)}^2+2\cdot 2\cdot \sqrt{7}\\ =4+7+4\sqrt{7}\\ =\boxed{11+4\sqrt{7}}\end{array}$

The simplified form of ${\left(2+\sqrt{7}\right)}^2$ is $11+4\sqrt{7}$ .