Question

express √3.5 geometrically​

Answer 1

Following steps:

From point , take point on left name as and take point on right name as. Bisect the line to get mid point of the line name as. Take as a center and as radius draw an semi circle. Using set-square draw perpendicular line through point which touch the circle line at.

Answer 2

Answer:

Represent √3.5 on number line

Step 1: Draw a line segment AB = 3.5 units

Step 2: Produce B till point C, such that BC = 1 unit

Step 3: Find the mid-point of AC, say O.

Step 4: Taking O as the centre draw a semi circle, passing through A and C.

Step 5: Draw a line passing through B perpendicular to OB, and cut semicircle at D.

Step 6: Consider B as a centre and BD as radius draw an arc cutting OC produced at E.

In right ΔOBD,

BD2 = OD2 – OB2

= OC2 – (OC – BC)2

(As, OD = OC)

BD2 = 2 OC x BC – (BC)2

= 2 x 2.25 x 1 – 1

= 3.5

=> BD = √3.5