All rational numbers are algebraic because every fraction a / b is a solution of bx - a = 0. Some irrational numbers such as 21/2 (the square root of 2) and 31/3 (the cube root of 3) are also algebraic because they are the solutions of x2 - 2 = 0 and x3 - 3 = 0, respectively. But not all real numbers are algebraic. Examples of this are π and e (the natural logarithm base).
If an algebraic number satisifies such an equation with a polynomial of degree n and not such an equation with a lower degree than the number is said to be an algebraic number of degree n.
It can be shown that if we allow the coefficients ai to be any algebraic number then the solution of the equation will also be an algebraic number.
If a complex number is not an algebraic number then it is called a transcendental number.