Question

represent √7.1 on number line and give steps of construction

Answer 1

Step-by-step explanation:

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

OB

2

=OA

2

+AB

2

=1

2

+1

2

=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

OD

2

=OC

2

+CD

2

=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

OF

2

=OE

2

+EF

2

=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.

solution