find any three irrational numbers between 4/7 and 5/7
Answers
Step-by-step explanation:
- 4/7 = 0.57142857143
- 5/7 = 0.71428571429
three irrational no. are 0.590590059000....,0.610610061000... and 0.63063006300
Hopes it may help You
please
mark
as
brilliant..
..
..
..
Step-by-step explanation:
Given:-
Numbers 4/7 and 5/7
To find:-
Find any three irrational numbers between 4/7 and 5/7
Solution:-
Given numbers are 4/7 and 5/7
Method -1:-
4/7 can be written as 0.571428581428...
5/7 can be written as 0.714285714285...
The required three irrational numbers are
0.5714289765..., 0.688965323..., 0.701242627...
Method-2:-
We know that
The irrational number between a and b is √(ab)
We have
a = 4/7
b= 5/7
First irrational number between 4/7 and 5/7
=> √[(4/7)×(5/7)]
=> √[(4×5)/(7×7)]
=>√(20/49)
=> (20/49)^(1/2)
Second irrational number between 4/7 and √(20/49)
=> √[(4/7)×(√(20/49)]
=>√[√{(16×20)/(49×49)}]
=>√[√(320/2401)]
=>√√(320/2401)
=> (320/2401)^(1/4)
Third irrational number between 4/7 and √√(320/2401)
=> √[(4/7)×(√√(320/2401)]
=>√√√[(320/2401)×(256/2401)]
=>√√√[(320×256)/(2401×2401)]
=>√√√(81920/5864801)
=> (81920/5864801)^(1/8)
The three irrational numbers are √(20/49) ,
√√(320/2401) , √√√(81920/5864801)
Answer:-
The required three irrational numbers are
0.5714289765..., 0.688965323..., 0.701242627...
or
The three irrational numbers are √(20/49) , √√(320/2401) √√√(81920/5864801)
or
The three irrational numbers are (20/49)^(1/2), (320/2401)^(1/4) , (81920/5864801)^(1/8)
Used formula:-
- The irrational number between a and b is √(ab)
- here ^ symbol means power
- The numbers are not in the form of p/q ,where p and q are integers and q≠0 called irrational numbers and they are denoted by Q' or S
- Non terminating and non recurring decimal is an irrational number.
- We can find infinitely many irrational numbers between two numbers by Dense Property