Question

Billy is trying to convince Sam that all square roots are irrational. To support his argument, Billy points out that 2003-01-01-00-00_files/i0290000.jpg, 2003-01-01-00-00_files/i0290001.jpg, 2003-01-01-00-00_files/i0290002.jpg, and 2003-01-01-00-00_files/i0290003.jpg are all irrational. Since this set of numbers contains the square roots of both prime and composite numbers as well as even and odd numbers, Billy argues that there is no number (prime, composite, even, or odd) whose square root is rational. Thus, all square roots must be irrational.

Where has Billy made his error?