Question

Find the square root of $\sqrt{24}$ using geometric method.

• A. 6.4
• B. 4.9
• C. 3.9
• D. 2.4

Answer 1

The correct option is B

4.9

$24=6\times 4$

i) Draw a ray AX of length greater than (6 + 4) cm.
ii) Cut off the part AB from AX equal to 6 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 6 and 4 is equal to $\sqrt{24}$.

Here, AB = 6 cm, BC = 4 cm.

The required mean proportional = BD and by scale, BD = 4.9 cm. (approx)

Hence, $\sqrt{24}=4.9cm$