If a is rational and b is irrational, when is a + b definitely irrational?

When a is any rational number

The sum of a rational number and an irrational number is always irrational. To see why, suppose a + b were rational. Since a is rational, subtracting a from the rational number a + b would make b = (a + b) - a rational, contradicting the given fact that b is irrational. Therefore a + b must be irrational for every rational value of a, including 0, 1, negative rationals, and fractions. Option A is correct. Option B and option C mention special choices that are sufficient but unnecessarily restrictive; the result does not depend on a being one particular rational number. Option D is the exact opposite of the closure argument. This property concerns addition, not multiplication or division, where different conditions may be needed.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.