Question

find three different irrational numbers between the rational numbers 6/13 and 5/19​

Answer 1

Answer:

6/13 = 0.46153846

5/19 = 0.26315789

Step-by-step explanation:

irrational number = 0.38374464748383 , 0.3964849292823 , 0.401773647394729

rational number = 0.30747484 , 0.418373939 , 0.42948484

Answer 2

Step-by-step explanation:

Given :-

The rational numbers 6/13 and 5/19

To find :-

Find three different irrational numbers between the rational numbers 6/13 and 5/19 ?

Solution:-

Given rational numbers are 6/13 and 5/19

We know that

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

First irrational number:-

We have a = 6/13 and b = 5/19

Irrational number = √[(6/13)×(5/19)]

=> √[(6×5)/(13×19)]

=> √(30/247)

2nd irrational number:-

We have a = 6/13 and b =√(30/247)

Irrational number =√[(6/13)×√(30/247)]

=>√[√[(30/247)×(36/169)]]

=>√√[(30×36)/(247×169)]

=>√(√(1080/41743))

3rd irrational number:-

We have a =6/13 and b = √(√(1080/41743))

The irrational number = √[(6/13)×√(√(1080/41743)]

=> √[√(√(1080/41743))×(36^2/169^2)]

=>√√√[(1080×36×36)/(41743×169×169)]

=>√√√(1399680/1192221823)

Method-2:-

The numbers are 6/13 and 5/19

6/13 = 0.461538...

5/19 = 0.2631578...

The three irrational numbers are 0.25678929... ,

0.356228263763.... , 0.456283738494...

Answer:-

The three irrational numbers are 0.25678929... ,

0.356228263763.... , 0.456283738494...

or

The three irrational numbers are √(30/247) ,

√(√(1080/41743)) , √√√(1399680/1192221823)

Used formula:-

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

• Non terminating and non recurring decimal is an irrational number.

• If n is a prime number then √n is an irrational number.