Question

Is a square root of 42 rational or irrational? explain

Answer 1

Answer: irrational

This is because we cannot write
`√(42)` as a fraction of two integers.

Something like
`√(49)` is rational because
`√(49) = 7 = (7)/(1)`

Use a calculator to determine that
`√(42) \approx 6.48074069840787...` where the decimal expansion goes on forever without a repeating pattern of some sort. In contrast,
`(23)/(99) = 0.232323... = 0.\overline{23}` means the "23" block repeats forever, so we have a rational number here.

In short:

decimal pattern repeats --> rational

decimal pattern doesn't repeat ---> irrational