Q. 2 A3.8( 4 Votes )

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

7

Answer :

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.


7 = 3.5 × 2


Construction steps:


1. Draw a line segment AX with length greater than (3.5 + 2 = 5.5 cm).



2. From A, mark a point B on AX such that AB = 3.5 cm and from B mark a point C such that BC = 2 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 = 3.5 cm and BC = 2 cm.


With the help of scale, we measure BD = 2.6 cm [Appx]


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