The existence of irrational numbers is best explained with an isosceles right triangle—that is, a triangle with two sides of an equal length that form a right angle.

Rational numbers can be expressed as the ratio of two integers, while irrational numbers, such as square roots of non-square numbers, cannot.

Real numbers are, in fact, pretty much any number that you can think of. This can include whole numbers or integers, fractions, rational numbers and irrational numbers.

The rest of the numbers on the number line are irrational numbers. These, too, can be divided into different categories—most of which we can’t even imagine.