Chapter 11.9, Problem 5WE

To determine

Simplify.

Answer to Problem 5WE

The simplified form of $\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)$ is $-62$ .

Explanation of Solution

Given information:

The expression $\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)$ .

Formula used:

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)$

As the expression resembles $\left(a+b\right)\left(a-b\right)$ ,

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

  $\begin{array}{l}\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\\ ={\left(\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2\\ =3-2\\ =\boxed{1}\end{array}$

The simplified form of $\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)$ is $1$ .