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Anybody can represent Root-3 on number line?

Draw a line. At a point A on the line construct a line which is perpendicular to the first line. Mark a point C on this line a distance of one unit from A.


Using the compass, draw an arc of a circle with radius 2 and center C so that the arc intersects the first line at B. Draw the line segment CB.

Now you have a right triangle with hypotenuse of length 2 units and one side of length 1 unit. Hence, by Pythagoras' Theorem

|CA| 2 + |AB| 2 = |BC| 2That is1 + |AB| 2 = 4and thus |AB| 2 = 3 and |AB| is the square root of 3.