HOW TO SHOW UNDER ROOT 8.5 IN NUMBER LINE
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Steps of construction of representing √8.5 on a number line:-
1) Draw a line 8.5 units, mark A as 8.5 and B as 0.
2) Extend the line segment AB 1 unit and name it as C.
3) Construct perpendicular bisector of AC and mark point of intersection as O.
4) With O as center, and OA as radius, complete the semi-circle.
5) From the point B, construct a perpendicular, intersecting the semi-circle at D.
6) Then, BD = root 8.5.
7) With B as center and BD as radius, draw an arc, intersecting the line at E.
8) E is a point root 8.5.
Proof :-
AB = 8.5 units
AC = 9.5 units
OA = OC = 9.5/2, OD = 9.5/2
BC = 1 units
OC = 9.5/2 units
OB = OC - BC = 9.5/2 - 1
Therefore, OD² = OB² + BD² (Pythagoras Theorem)
So, BD = root 8.5.
Proved.
1) Draw a line 8.5 units, mark A as 8.5 and B as 0.
2) Extend the line segment AB 1 unit and name it as C.
3) Construct perpendicular bisector of AC and mark point of intersection as O.
4) With O as center, and OA as radius, complete the semi-circle.
5) From the point B, construct a perpendicular, intersecting the semi-circle at D.
6) Then, BD = root 8.5.
7) With B as center and BD as radius, draw an arc, intersecting the line at E.
8) E is a point root 8.5.
Proof :-
AB = 8.5 units
AC = 9.5 units
OA = OC = 9.5/2, OD = 9.5/2
BC = 1 units
OC = 9.5/2 units
OB = OC - BC = 9.5/2 - 1
Therefore, OD² = OB² + BD² (Pythagoras Theorem)
So, BD = root 8.5.
Proved.
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