Question

find six irrational naumbers between 0.3 and 0.42​

Answer 1

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