How are square roots and rational and irrational numbers related?

Answer 1

A rational number is one that can be expressed as a ratio of two integers, p/q where q > 0. In decimal form, it has a terminating or recurring representation.

An rational number is a number than cannot be expressed as a ratio of two integers. In decimal form, it has a infinitely long, non-recurring representation.

A square root can be either rational or irrational or neither.

Examples:

The square roots of 4 are -2 and +2, both rational.

The square roots of 2.25 are -1.5 and +1.5, both rational.

The square roots of 2 are -1.41421... and +1.41421, both irrational.

The square roots of -2 are -1.41421...*i and +1.41421*i, both imaginary.