Question

find any three irrational numbers between 4/7 and 5/7

Answer 1

Step-by-step explanation:

• 4/7 = 0.57142857143
• 5/7 = 0.71428571429

three irrational no. are 0.590590059000....,0.610610061000... and 0.63063006300

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Answer 2

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