Question

how to plot pi on a number line

Answer 1

While square roots can be constructed, a line with length corresponding to pi cannot be constructed, due to pi being transcendental. You can, however, construct a circle of unit diameter whose circumference will be pi. If you just want the decimal value of pi, many numerical algorithms exist that converge to multiples of pi, including the Newton-Raphson method, or Taylor series of trigonometric functions.