Billy is trying to convince Sam that all square roots are irrational. To support his argument, Billy points out that 2, 6, 77, and 15 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?
A He has made no error. All square roots are irrational.
B Neither V nor V6 are irrational. His argument about the square root of even numbers is
invalid.
C. Neither V6 nor V15 are irrational. His argument about the square root of composite numbers
is invalid.
D. He has failed to consider square roots of perfect squares, such as V. 4, or 25, which
simplify to be integers, and thus rational numbers.
Please select the best answer from the choices provided