Which statement correctly classifies the numbers sqrt(2), 3/5, and pi as rational or irrational?

Which statement correctly classifies the numbers sqrt(2), 3/5, and pi as rational or irrational?

• A. sqrt(2) irrational; 3/5 rational; pi irrational
• B. sqrt(2) irrational; 3/5 irrational; pi rational
• C. sqrt(2) rational; 3/5 rational; pi irrational
• D. sqrt(2) irrational; 3/5 rational; pi rational

Answer: (A)

Rational numbers are those that can be written as a ratio of two integers. Irrational numbers cannot be written that way and usually don’t have decimal forms that terminate or repeat. sqrt(2) can’t be expressed as a fraction of integers, so it’s irrational. The fraction 3/5 is already a ratio of integers with a nonzero denominator, so it’s rational. Pi’s decimal expansion goes on forever without repeating, which means it’s irrational. So the statement that matches these classifications is: sqrt(2) irrational; 3/5 rational; pi irrational.

Rational numbers are those that can be written as a ratio of two integers. Irrational numbers cannot be written that way and usually don’t have decimal forms that terminate or repeat.

sqrt(2) can’t be expressed as a fraction of integers, so it’s irrational. The fraction 3/5 is already a ratio of integers with a nonzero denominator, so it’s rational. Pi’s decimal expansion goes on forever without repeating, which means it’s irrational.

So the statement that matches these classifications is: sqrt(2) irrational; 3/5 rational; pi irrational.