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Which of the following statements is TRUE?

Competition practiceNumber & Arithmetic
  • AEvery real number is a rational number
  • BThe difference of two irrational numbers is always irrational
  • CThe sum of a rational number and an irrational number is always irrational
  • DBetween any two rational numbers there are only finitely many rational numbers

Step-by-Step Solution

If a rational r plus an irrational i were rational, then i = (r + i) − r would be a difference of two rationals and so rational — impossible. The others fail: √5 is real but not rational; √3 − √3 = 0 is rational; and between any two rationals lie infinitely many more (keep taking averages).
Answer: C) The sum of a rational number and an irrational number is always irrational

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