Question

Which of the following addition or subtraction of irrational numbers will not result into an irrational number.

• A. $(2+\sqrt{8})+(5+\sqrt{8})$
• B. $(2+\sqrt{8})-(5+\sqrt{8})$
• C. $(\sqrt{9}-\sqrt{2})+\frac{(\sqrt{16}+\sqrt{8})}{2}$

Answer 1

Answer: (B), (C)

$(\sqrt{9}-\sqrt{2})+\frac{(\sqrt{16}+\sqrt{8})}{2}$

First, we will solve $(2+\sqrt{8})+(5+\sqrt{8})\Rightarrow (2+2\sqrt{2})+(5+2\sqrt{2})=7+4\sqrt{2}$

Now, we will solve $(2+\sqrt{8})-(5+\sqrt{8})\Rightarrow (2+2\sqrt{2})-(5+2\sqrt{2})=-3$

Now, we will solve $(\sqrt{9}-\sqrt{2})+\frac{(\sqrt{16}+\sqrt{8})}{2}\Rightarrow (3-\sqrt{2})+(2+\sqrt{2})=5$