Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., Ï<sup>2</sup>). For example, by truncating the decimal expansion of â2 (square root of 2), show that â2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that â2 is irrational.