Question

Find the square root of 10 using geometric method.

• A. 4
• B. 1
• C. 2.5
• D. 3.2

Answer 1

The correct option is D

3.2

We know that $10=5\times 2$
Find the mean proportional of 5 and 2 to find $\sqrt{10}$.

Steps of Construction:
i) Draw a ray AX of length greater than (5 + 2) cm.
ii) Cut off the part AB from AX equal to 5 cm and the part BC from BX equal to 2 cm.
iii) Draw a perpendicular bisector PQ of AC. Let PQ intersect AC at O.
iv) Draw a semi-circle by taking centre at O and radius equal to OA or OC.
v) Draw a perpendicular on OC at B, which intersects the semi circle at the point D.
Join B and D.
BD is the mean proportional, which is also the $\sqrt{10}=3.2$.