Question

Q : Show how UNDERROOT √11 can be represent on the number line ?





I will mark uhh brainlist...​

Answer 1

Step-by-step explanation:

Steps

1. Draw A line XY

2. On XY Draw a line segment AB = 11 cm

3. On XY draw BC = 1 cm(take C on right of AB ,I.e, such that AC = 12cm)

4. Find the midpoint of AC and mark it as O.

5. Taking OA = OC as radius and O as centre draw a semicircle on XY.

6. From B draw a perpendicular intersecting the semicircle at M.

7. Taking BM as radius and B as centre draw an arc intersecting XY at P in the direction of BC.

If B is origin = 0 , then P represent √11 on the number line XY.

Proof of method

OA = OC = (11+1)/2 cm= 6cm.

OB = OC - BC = (6-1) cm= 5 cm

in ∆OBM ,

OM = OC = 6 cm(radii of same semicircle)

OB = 5cm.

therefore using Pythagoras theorem

OM^2 = OB^2 + BM ^2

=> 36 = 25 + BM^2

=> BM = √11

Now BM = BP so BP = √11