Question

Find the square root of $\sqrt{28}$ using geometric method.

• A. 6.4
• B. 4.9
• C. 3.9
• D. 5.3

Answer 1

The correct option is D 5.3

$28=7\times 4$

i) Draw a ray AX of length greater than (7 + 4) cm.

ii) Cut off the part AB from AX equal to 7 cm and the part BC from BX equal to 4 cm.

iii) Draw a perpendicular bisector PQ of AC. PQ intersects 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.
vi) Join B and D.
vii) BD is the required mean proportional.

So, mean proportional of 7 and 4 is equal to $\sqrt{28}$.

Here, AB = 7 cm, BC = 4 cm.

The required mean proportional = BD and by scale, BD = 5.3 cm. (approx)

Hence, $\sqrt{28}=5.3cm$