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Represent √2 ,√3 , √5 ,√7 , √10 , √11, √13 ,√17 on Number line.
Also give the justification for each construction.
Answers
Step-by-step explanation:
√2:-
Draw a unit square OABC at O on a number line with each side 1 unit in length
By Pythagoras theorem
OB = √(OA^2+AB^2)
=>OB =√(1^2+1^2)
=>OB=√(1+1)
OB=√2
√3:-
Draw √2 on the number line as shown above and Consider OD =√[(√2)^2+1^2]
OD =√(2+1)
OD=√3
√5:-
Draw a square OABC at O of 2 units and 1 units and OB =√(2^2+1^2)
OB=√(4+1)
OB=√5
√7:-
Draw √3 as shown above
Consider CD of 2 units then
OD =√[(√3)^2+2^2)]
OD =√(3+4)
OD =√7
√10:-
Draw a square OABC at O of 3 units and 1 units
OB =√[3^2+1^2]
OB =√(9+1)
OB=√10
√11:-
Draw √2 on the number line as shown in the figure.
Draw a line segment at B of 3 units
OD =√[(OB)^2+(BD)^2]
OD =√(√2)^2+(3)^2
OD=√(2+9)
OD=√11
√13:-
Draw a square OABC square if 3 units and 2 units
OB=√[OB^2+AB^2]
OB=√(3^2+2^2)
OB=√(9+4)
OB=√13
√17:-
Draw a square OABC at O of 4 units and 3 units
Now OB =4 units
AB=1 units
By Pythagoras theorem
OB^2=OA^2+AB^2
OB=√[OA^2+AB^2]
OB=√(4^2+1^2)
OB=√(16+1)
OB=√17 units
We locate on √n for any positive integers n, after √(n-1) has been located on the number line .
Step-by-step explanation:
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