Representation of irretional number (√5) and (√7) on number line
Answers
Answer:
Draw a number line and mark 0, 1, 2, 3, ....etc.
Mark 0 as point O and 2 as B.
Now from B, draw a perpendicular AB of length 1 unit.
Join OA. ...
Again From A, draw a perpendicular AC of length 1 unit.
Join OC. ...
Again From C, draw a perpendicular CD of length 1 unit.
Join OD.
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.
