Question

State true or false:

There can be a pair of irrational numbers whose sum is irrational such as

$\sqrt{3}+2$ and $5+\sqrt{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

To get the sum as irrational, both the numbers need to have an irrational part which are different from each other.
Example, the given pair of numbers $\sqrt{3}+2$ and $5+\sqrt{2}$ have the sum $\sqrt{3}+2+5+\sqrt{2}=7+\sqrt{2}+\sqrt{3}$ which is an irrational number too.

Hence, the given statement is true and option $A$ is correct.