Represent `sqrt(3. 5)`on the real number line.

Explanation

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 `/_\ OBD, BD^2 = OD^2 – OB^2 `
=` OC^2 – (OC – BC)^2 `
`(As, OD = OC) `
` BD^2 = 2 OC x BC – (BC)^2`
=` 2 x 2.25 x 1 – 1 = 3.5 `
=> `BD = (sqrt 3.5)`.