Irrational or Rational

Worksheet Description

This worksheet is designed to help students practice classifying numbers as rational or irrational. It presents a list of various types of numbers, including square roots, cube roots, and decimals. The students must determine whether each number is rational, meaning it can be expressed as a fraction of two integers, or irrational, meaning it cannot be expressed as such a fraction and has a non-terminating, non-repeating decimal expansion. The exercise includes both perfect squares and non-perfect squares, as well as decimals that either terminate, repeat, or neither.

The worksheet aims to teach students the distinction between rational and irrational numbers, a foundational concept in mathematics. By evaluating square roots and cube roots, students learn to recognize perfect squares and perfect cubes, which are rational, and contrast them with roots that do not resolve to rational numbers. With the decimals, students are challenged to identify patterns in decimal expansions that signify rationality, such as termination or repetition, versus those that signify irrationality. This practice strengthens their number sense and prepares them for more complex mathematical studies involving the real number system.