Rational & Irrational Numbers

A rational number can be written as a ratio of two integers — every fraction, every terminating or repeating decimal. An irrational number cannot — its decimal runs forever with no pattern, like $\sqrt{2}$ or $\pi$.

The Regents questions here are mostly about closure — what kind of number you get back from an operation:

• The sum or product of two rationals is always rational.
• The sum of a rational and an irrational is irrational; so is the product of a nonzero rational and an irrational.
• Operations on two irrationals are not guaranteed either way — $\sqrt{2}\cdot \sqrt{2} = 2$ is rational, but $\sqrt{2}\cdot\sqrt{3} = \sqrt{6}$ is irrational.

These are real, released Regents questions.