Irrational Numbers

An Irrational Number is a real number that cannot be written as a simple fraction, because there is not a finite number of numbers when written as a decimal. Instead, the numbers in the decimal would go on forever, without repeating.

Famous Irrational Numbers

		Pi is a famous irrational number. People have calculated Pi to over a quadrillion decimal places and still there is no pattern. The first few digits look like this: 3.1415926535897932384626433832795 (and more ...)
		The number e (Euler's Number) is another famous irrational number. People have also calculated e to lots of decimal places without any pattern showing. The first few digits look like this: 2.7182818284590452353602874713527 (and more ...)
		The Golden Ratio is an irrational number. The first few digits look like this: 1.61803398874989484820... (and more ...)
		Many square roots, cube roots, etc are also irrational numbers. Examples: √3 1.7320508075688772935274463415059 (etc) √99 9.9498743710661995473447982100121 (etc)

But √4 = 2 (rational), and √9 = 3 (rational) ...

... so not all roots are irrational.

 

Note on Multiplying Irrational Numbers

Have a look at this:

• π × π = π² is irrational
• But √2 × √2 = 2 is rational

So be careful ... multiplying irrational numbers might result in a rational number!