Constructible Numbers

What does it mean for a number to be constructible?

Given segments of lengths x and y, there are five “operations” that can be constructed: x + y, x – y, x*y, y/x, and Öx or Öy. Therefore, the constructible numbers (numbers that can be constructed) are those that can be found using a finite number of applications of the constructible operations.

If a number is transcendental, then it is not the root of a rational equation. Therefore, we cannot arrive at a transcendental number by applying the five operations a finite number of times. Thus, transcendental numbers are not constructible.