Practice Real Numbers in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The complete set of all rational and irrational numbers, filling every point on the continuous number line.

Any number you can point to on an infinitely precise number line.

Example 1

easy
Classify each number as rational or irrational, and state whether it is a real number: -7, \sqrt{9}, \sqrt{7}, \pi.

Example 2

medium
Show that between any two distinct real numbers a and b (with a < b), there exists another real number.

Example 3

easy
Which of the following are NOT real numbers? \sqrt{-4}, -\sqrt{4}, \sqrt[3]{-8}, \frac{1}{0}.

Example 4

medium
Give one example of a real number between \sqrt{2} and \sqrt{3}.