Chapter 7.4, Problem 81HP

To determine

To describe step by step how to multiply radical expressions with two terms

Explanation of Solution

Consider two radical expressions, $(\sqrt{2}+5)$ and $(\sqrt{2}-3)$

To multiply the given radical expression use distributive property.

  $\begin{array}{l}\Rightarrow (\sqrt{2}+5)(\sqrt{2}-3)\\ \Rightarrow (\sqrt{2}\times \sqrt{2})+(\sqrt{2}\times -3)+(5\times \sqrt{2})+(5\times -3)\end{array}$

Now simplify the above expression.

  $\Rightarrow (2)+(-3\sqrt{2})+(5\sqrt{2})+(-15)$

Combine the like terms.

  $\Rightarrow 2-15-3\sqrt{2}+5\sqrt{2}$

Simplify the above expression.

  $\Rightarrow -13+2\sqrt{2}$

Conclusion:

Therefore, the product of radicals with two terms can be solved with the above steps.