Give an example of a square root that is not a rational number?

Answer 1

The square root of 2 is irrational because it cannot be expressed as a fraction in which the numerator and denominator are both integers.

Another way of saying this is that the square root of 2 will have infinite decimal places in any a number system of any radix (base 10, base 2, base 3, base 16, etc)

This should not be confused with imaginary numbers. Rational and Irrational Numbers together combine to make the Real numbers, imaginary numbers are, however, not Real. Imaginary numbers are those that can be expressed as a Real number multiplied by the square root of negative 1 (also known as i or j)

So, strictly speaking, both sqrt(2) and sqrt(-1) are "not rational numbers", however, they are not both "irrational" numbers.