To locate: the point on a number line, explain the location of and , list some other irrational numbers can be located in same manner.
Given number line
If in a right triangle, the base=height=1 unit, then the hypotenuse is units, by the Pythagorean theorem.
So, consider one unit from the origin along the positive direction of the axis and from there, consider the point at a distance of one unit parallel to the axis. We then get to a point which is units from the origin.
Consider the distance to be radius of a circle, which intersects the axis at units.
Thus, the point of intersection of the circle with the axis is units.
Similarly, 2 units from the origin along the axis and 1 unit parallel to axis, the point we reach will be units from the origin.
So by drawing a circle using this distance as the radius, it intersects the axis at units.
Thus, can be traced on the axis.
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