Question

How to find square root of x on the number line geometrically

Answer 1

To find √x for any given positive real number 'x' geometrically.

For example, let us assume x = 4.5

We shall now find √4.5 geometrically.

PQ = 4.5 on a number line

Mark the distance 4.5 units from a fixed point P on a given line to obtain a point Q such that PQ = 4.5 units.

From Q, mark a distance of 1 unit and mark the new point as R.

Find the mid-point of PR and mark that point as O.

Draw a semicircle with center O and radius OR.

Draw a line perpendicular to PR passing through Q and intersecting the semicircle at S.

Then, QS = √4.5

Square root of (4.5)