Question

Give an example of two irrational numbers, whose sum is an irrational number.

• A. $2\sqrt{5},3\sqrt{5}$
• B. $2\sqrt{5},-2\sqrt{5}$
• C. $2+\sqrt{5},2-\sqrt{5}$
• D. $2+\sqrt{5},3-\sqrt{5}$

Answer 1

Answer: (A)

$2\sqrt{5},3\sqrt{5}$

Consider option $A$.

The number are $2\sqrt{5}$ and $3\sqrt{5}$.
Their sum $=2\sqrt{5}+3\sqrt{5}=5\sqrt{5}$, which is an irrational number.

Consider option $B$.

The number are $2\sqrt{5}$ and $-2\sqrt{5}$.
Their sum $=2\sqrt{5}+(-2\sqrt{5})=0$, which is a rational number.

Consider option $C$.

The number are $2+\sqrt{5}$ and $2-\sqrt{5}$.
Their sum $=2+\sqrt{5}+2-\sqrt{5}=4$, which is a rational number.

Consider option $D$.

The number are $2+\sqrt{5}$ and $3-\sqrt{5}$.
Their sum $=2+\sqrt{5}+3-\sqrt{5}=5$, which is a rational number.

Therefore, option $A$ is correct.