find six irrational naumbers between 0.3 and 0.42
Answers
Step-by-step explanation:
Given :-
0.3 and 0.42
To find :-
Find six irrational naumbers between 0.3 and 0.42 ?
Solution :-
General method:-
Given numbers are 0.3 and 0.42
The Irrational numbers are 0.3335789...,
034671010112...,0.351235...,0.36768...,
0.39101100...,0.40414242....
Formula method:-
Given numbers are 0.3 and 0.42
=> 0.3
=> 3/10
=> (3/10)×(10/10)
=> (3×10)/(10×10)
=> 30/100
and
0.42
=> 42/100
We know that
The irrational number between a and b = √(ab)
1) Irrational number between 0.3 and 0.42
=> √[(30/100)×(42/100)]
=> √[(30×42)/10000]
=> √(1260/10000)
=> √(4×5×7×9)/(10000)
=> 2×3(√35)/100
=> (6/100)√35
=> (3/50)√35
Irrational number = √(1260/10000) or (3/50)√(35)
2) The rational number between 30/100 and √(1260/10000)
=> √[(30/100)×√(1260/10000)]
=> √√[(900/10000)×(1260/10000)
=> √√(900×1260/(100000000)
=>√√(1134000/100000000)
=> [√√(113400000)]/100
Using this formula we get irrational numbers
Used formulae:-
- The irrational number between a and b is √(ab)
Points to know:-
- The numbers can not be written in the form of p/q ,where p and q are integers and q≠0 called irrational numbers . They are denoted by Q' or S.
- The decimal expansion of an irrational number is non terminating and non recurring decimal.
Ex:-1) √2,√3....
2) π , e
3)1.1010001000000,...
4) log 2, log 3,...
Densitive Property:-
- There are infinitely number of irrational numbers between two numbers