Represent the real number on the number line.

Step-by-step solution

Draw a number line l, mark the point O, A and B such that OA = AB = 1 unit. Draw BC ⊥ l such that BC = 1 unit. Join OC. In right-angled 2206OBC, OC 2 = OB 2 + BC 2 = 2 2 + 1 2 ∴ OC = units Taking O as centre and OC as radius, draw an arc which intersects line l at D. ∴ Point D represents and OD = units. Now, draw DE ⊥ l such that DE = 1 unit. Join OE. In right-angled 2206OED, using Pythagoras theorem, OE 2 = OD 2 + DE 2 = ( ) 2 + 1 = 5 + 1 = 6 ∴ OE = units Taking O as centre and OE as