Click here to purchase the entire book in PDF format. Irrational Numbers What happens if you have a number that doesn't start repeating, no matter how many numbers you have? Take a number like the square root of 2 for example. This is a number that, when you multiply it by itself, results in the number 2. This number is approximately 1.4142. But, if we multiply 1.4142 by 1.4142, we get 1.99996164 - so 1.4142 isn't exactly the square root of 2. In fact, if we started calculating the exact square root of 2, we'd result in a number that keeps going forever after the decimal place and never repeats. Numbers like this ($\pi$ is another one...) that never repeat after the decimal are called irrational numbers