Question

find four irrational number between 3/8 and 6/5

Answer 1

Answer:

19/48

Step-by-step explanation:

7/16

23/48

9/16

29/16

Answer 2

Step-by-step explanation:

Given :-

3/8 and 6/5

To find:-

Find four irrational number between 3/8 and 6/5?

Solution:-

Method-1:-

Given numbers are 3/8 and 6/5

3/8 = 0.375

6/5 = 1.2

So the required irrational numbers are :

0.375678...,0.38901001000...,1.161161117..., 1.19889888999...

Method-2:-

Given numbers are 3/8 and 6/5

We know that

The irrational number between a and b is √(ab)

i) Let a = 3/8 and b = 6/5

The first irrational number between 3/8 and 6/5

=> √[(3/8)×(6/5)]

=> √[(3×6)/(8×5)]

=> √(18/40)

=> √(9/20)

ii) Let a = 3/8 and b = √(9/20)

The second irrational number

= √[(3/8)×√(9/20)]

=> √√[(9/20)×(9/64)]

=>√√[(9×9)/(20×64)]

=> √√(81/1280)

iii) Let a = 3/8 and b =√√(81/1280)

The third irrational number

=> √[(3/8)×√√(81/1280)]

=> √√√[(81/1280)×(81/4096)]

=>√√√[(81×81)/(1280×4096)

=> √√√(6561/5242880)

iv)Let a = 3/8 and b=√√√(6561/5242880)

The fourth irrational number

=> √[(3/8)×√√√(6561/5242880)]

=> √√√√[(6561/5242880)×(6561/4096)]

=> √√√√[(6561×6561)/(5242880×4096)]

=>√√√√(43046721/21457107840)

Answer :-

The four irrational numbers between the given numbers by general method are 0.375678...,0.38901001000...,1.161161117..., 1.19889888999...

The four irrational numbers between the given numbers by formula method are √(9/20), √√(81/1280), √√√(6561/5242880), √√√√(43046721/21457107840)

Used formulae:-

• The irrational number between a and b is √(ab)
• There are infinitely number of many irrational numbers between two numbers.