This also means that the decimal expansion of an irrational number goes on forever.

Square roots, cube roots and other roots can all be irrational numbers. Transcendental numbers like pi and e are also irrational.

Raising an integer to a fraction will give an irrational number (unless it comes out exactly and gives an integer.) For example:

2

^{1/2}= √2 = 1.41421356...

5

^{3/2}= (√5)

^{3}= 11.180339877...

A real number that cannot be expressed as a rational number, ie. a number that cannot be written as a simple fraction - the decimal goes on forever without repeating.

ReplyDeleteExample: Pi is an irrational number