Question

Represent √7 on the number line

Answer 1

Steps:

Let O be the origin on the line l.  

Let A be on the line such that OA=1.  

Draw AB perpendicular to OA at A such that AB=1. Then

OB2=OA2+AB2=12+12=2 Thus OB=2.  

With O as centre and OB as radius draw an arc cutting the line at C.  

Then OC=OB=2  

Again draw CD prependicular to l such that CD=1. Then  

OD2=OC2+CD2=2+1=3. Thus OD=3.  

Draw an arc with O as centre and OD as radius to cut l in E. Then OE=OD=3.

Draw EF prependicular to l at E such that EF = 2 and join OF. Now

OF2=OE2+EF2=3+4=7.

Hence OF=7. With O as centre and OF as radius, cut l at G.  

Then OG=OF=7.

Thus G represents 7 on the line l.

Thanks!