Practice Irrational Numbers in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An irrational number is a real number that cannot be expressed as a ratio of two integers \frac{p}{q}; its decimal expansion goes on forever without repeating any fixed block of digits.
\pi and \sqrt{2} go on forever without any pattern—you can't write them as a fraction.
Example 1
easyClassify each number as rational or irrational: \sqrt{16}, \sqrt{5}, 0.75, \pi.
Example 2
mediumShow that \sqrt{2} lies between 1.4 and 1.5, then estimate it to one decimal place.
Example 3
mediumProve that \sqrt{3} is irrational by contradiction.
Example 4
easyIs \sqrt{49} + \sqrt{3} rational or irrational? Explain.
Example 5
easyIs 3 + \sqrt{7} rational or irrational?