Final answer:
To obtain a rational number by adding a number to the square root of 2 (sqrt(2)), you must add its additive inverse, which is -sqrt(2). The result of this addition is the rational number 0.
Step-by-step explanation:
To answer the question about which number can be added to sqrt(2) to get a rational number, we must acknowledge that sqrt(2) is an irrational number. By the property of irrational numbers, the only way to obtain a rational result by adding a number to an irrational number is to add its additive inverse. Since the additive inverse of sqrt(2) is -sqrt(2), adding these two numbers will yield a rational result, which is 0. There is no other specific rational number that can universally be added to sqrt(2) to result in a rational number, as the sum of a rational number and an irrational number is always irrational.