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Answer:
The required number line for
2
3
5
2
3
and
5
Step-by-step explanation:
Explanation:
Draw a number line .
Taking OA = 1 unit
Draw AB perpendicular on OA
such that AB = 1 units and let OA = 1 unit
Step1:
Now from pythagoras theorem
=
(
)
2
+
(
)
2
OB=
(OA)
2
+(AB)
2
=
1
2
+
1
2
1
2
+1
2
=
2
2
Now taking length of OB and from the centre draw an arc through compass which cut the number line .
So , the intersect point on the number line is
2
2
For
3
3
:
Draw CB perpendicular on OB
Such that OB =
2
2
unit and let CB = 1 unit .
Therefore by pythagoras theorem
=
1
2
+
2
2
OC=
1
2
+
2
2
=
3
3
Now taking length of OC and draw an arc through compass which cut the number line .
So , the intersect point on the number line is
3
3
Similarly for
5
5
:
Draw DC perpendicular on OC
such that OC =
3
3
unit and let DC =
2
2
.
By pythagoras theorem
=
2
2
+
3
2
OD=
2
2
+
3
2
=
5
5
.
Now taking length of OD and draw an arc through compass which cut the number line .
So , the intersect point on the number line is
5
5
.
Final answer:
Hence , here we represent the real number
2
3
5
2
3
and
5
on the number line .