Question

How do you plot `sqrt46` on the decimal number line as accurately as possible?

Answer 1

Here's how you could do it geometrically...

Explanation:

Draw a circle with centre `(0, 45/2)` with radius `47/2`.

This will pass though the points `(0, -1)` and `(0, 46)` on the `y` axis and the points `(-sqrt(46), 0)` and `(sqrt(46), 0)` on the `x` axis.

graph{(x^2 + (y-45/2)^2 - 47^2/4)((x-sqrt(46))^2+y^2-0.01)((x+sqrt(46))^2+y^2-0.01) = 0 [-9.83, 10.17, -3.28, 6.72]}