What is the difference between an irrational and transcendental number?
Transcendental numbers are irrational, just like squares are rectangles and apples are fruit. Not all irrational numbers are transcendental though. The non-transcendental numbers are called algebraic. They include all the numbers that can be solutions of a nice polynomial equation with integer coefficients. Things like the square root of 2 (it’s the solution of x^2 – 2 = 0) and the cube root of 3 (the solution of x^3 – 3 = 0) are algebraic. If you have a transcendental number, there won’t be any polynomial equations that your number is a solution of. The most famous are pi an e.
