Question

Locate √11 on the number line

Answer 1

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


   Þ  OT²    =  MT ² -  OM²

  Þ  OT²    =   6²    -   5²

   Þ  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.