Question

Find the value of $\sqrt{4}$ using geometric method.

• A. 2
• B. 1
• C. 2.1
• D. 2.9

Answer 1

The correct option is A

2

We know that $4=4\times 1$. So, we can construct the mean proportional of two line segments of lengths 4 cm and 1 cm, which will be the required square root of 4.

Method of construction:

Let us consider the two numbers as 'a' and 'b', where a = 4cm and b = 1cm.
(i) Let us draw a ray AX of length greater than (a+b) = (4+1) cm
(ii) Let us cut off the part AB from AX equal to 'a' cm (4cm) and the part BC from BX equal to 'b' cm (1cm).



(iii) Let us draw a perpendicular bisector PQ of AC. Let PQ intersects AC at O



(iv) Let us draw a semi-circle by taking centre at O and radius equal to OA or OC.



(v) Let us now draw a perpendicular on OC at B, which intersects the semi-circle at the point D.



(vi) Let us join B and D.



Here AB = 4cm and BC = 1cm and BD is the required mean proportional of AB and BC. By scale, BD = 2cm.
$\therefore \sqrt{4}=2cm$