Question

the sum of two irrational numbers is _blank_ a rational number.

which word correctly fills in the blank to create a true statement?

sometimes
always
never

Explanation:

Step1: Find a case where the sum is irrational

$$\sqrt{2} + \sqrt{2} = 2\sqrt{2}$$

Step2: Find a case where the sum is rational

$$\sqrt{2} + (-\sqrt{2}) = 0$$

Step3: Determine the correct statement

Since the sum can be either rational or irrational, it is sometimes a rational number.

Answer:

sometimes