Let us determine the square roots of the following numbers by geometric method:

24

We know, that mean proportion of two number ‘a’ and ‘b’ is . In order to find the square root of each number, we will factorize them into two factors and then we will find the mean proportion of two numbers.

24 = 6 × 4

Construction steps:

1. Draw a line segment AX with length greater than (6 + 4 = 10 cm).

2. From A, mark a point B on AX such that AB = 6 cm and from B mark a point C such that BC = 4 cm

3. Draw the perpendicular bisector of AC, such that it cuts AC at O.

4. Taking OA = OC as radius and O as center draw a semicircle.

5. Draw BD ⊥ AC such that, point D lies on the semicircle and

Here, BD is the mean proportional of AB and BC, and By construction AB = 6 cm and BC = 4 cm.

With the help of scale, we measure BD = 4.9 cm [Appx]