An irrational number is a number that is not rational. It cannot be written as a positive fraction, a negative fraction, or zero.

Pi (\(\pi\)) and \(\sqrt2\) are examples of irrational numbers.

The legs of a right triangle are the sides that make the right angle. 

Here are some right triangles. Each leg is labeled.

A rational number is a number that can be written as a positive fraction, a negative fraction, or zero. It can be written in the form \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b\) is not equal to 0.

For example, 0.7 is a rational number because it can be written as \(\frac{7}{10}\).

Some examples of rational numbers: \(\frac74,0,\frac63,0.2,\text-\frac13,\text-5,\sqrt9\)

A repeating decimal has digits that keep going in the same pattern over and over. The repeating digits are marked with a line above them.

• The decimal representation for \(\frac13\) is \(0.\overline{3}\), which means 0.3333333 . . . .
• The decimal representation for \(\frac{25}{22}\) is \(1.1\overline{36}\), which means 1.136363636 . . . .

The square root of a positive number \(n\) is the positive number whose square is \(n\). It is also the side length of a square whose area is \(n\). The square root of \(n\) is written as \(\sqrt{n}\).

The square root of 16 is written as \(\sqrt{16}\). Its value is 4 because \(4^2\) is 16.

\(\sqrt{16}\) is also the side length of a square that has an area of 16.