Question

Represent root 11.3 on number line

Answer 1

Diagram shows procedure.

Draw AF horizontally of 13.3 cm.  Mark with compass from A points B, C D, and E with AB = 1 cm, AC = 2 cm, AD = 11.3 cm, and AE = 12.3 cm.

Draw perpendicular bisectors PBP' and QEQ' of AC and DF respectively. BE = 11.3 cm.

Using the standard procedure for angular bisector bisect angle DEQ' and angle CBP'. These two bisectors meet at G.  Now BG  = EG = sqroot(11.3) cm.
 
Draw an arc from B with radius BG to cut BD at H.   BH is the line with length = sqroot(11.3) cm.