Chapter 7.4, Problem 80HP

To determine

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

Explanation of Solution

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

To add the given radical expressions, combine the like terms.

The terms with the roots and the normal integers are to be combined separately.

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

Simplify the above expression using basic arithmetic operations.

  $\Rightarrow 2+\sqrt{2}+\sqrt{3}$

Only like radicands can be added. If the radicands are different, they cannot be added.

Therefore, $(\sqrt{2}+5)+(\sqrt{2}-3)=2+\sqrt{2}+\sqrt{3}$

Conclusion:

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