Question

Show that root 10 and root 11 on number line

Answer 1

Step-by-step explanation:

• √10  -- We can do it by using Pythagoras Theorem.

We can write √10 = √(9 + 1)

=> √10 = √(32 + 1)                  

Construction

1. Take a line segment AO = 3 unit on the x-axis.   (consider 1 unit = 2cm)    

2. Draw a perpendicular on O and draw a line OC = 1 unit  

3. Now join AC with √10.  

4. Take A as center and AC as radius, draw an arc which cuts the x-axis at point E.

5. The line segment AC represents √10 units.

• √11 - First draw a number line with center O. Take a point P with

distance OP=11 unit.

Take another point Q with distance OQ=1 unit.

So PQ=OP+OQ=11+1=12

Take a point M where M is the midpoint of PQ.

Therefore PM=MQ= ½PQ=6

Draw an arc with center M from point Q and draw a line perpendicular to PQ   from point O which cuts the arc at point T.

As PQ and MT  are radius of same arc, so MT=MQ=6

OM=OP-PM=11-6=5

Now  ΔMOT is a right angled triangle with  <MOT=90°

By using Pythagoras Theorem,

MT ²   =    OM² + OT²

OT²    =  MT ² -  OM²

OT²    =   6²    -   5²

 OT     =   √11

Now drawing an arc with center O from point T to PQ,we get point R where the arc intersects the line PQ.

Since OT and OR both are radii  of same arc,

So  OT=OR=√11

Therefore √11 is placed at point R on number line.

Answer 2

Answer:

1. Take a line segment AO = 3 unit on the x-axis.   (consider 1 unit = 2cm)    

2. Draw a perpendicular on O and draw a line OC = 1 unit  

3. Now join AC with √10.  

4. Take A as center and AC as radius, draw an arc which cuts the x-axis at point E.