Question

represent the following on a number line. 7
$\sqrt{7}$
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Answer 1

Answer:

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.