Question

find two irrational numbers between 4 and 5​

Answer 1

Answer:

The 5 irrational numbers between 4 and 5 are as follows:

a=4.101001000....

b=4.20002000....

Answer 2

Step-by-step explanation:

Given:-

4 and 5

To find :-

Find two irrational numbers between 4 and 5 ?

Solution :-

Given numbers are 4 and 5

We know that

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

Finding the irrational number between 4 and 5:-

Let a = 4 and b = 5 then

The irrational number between 4 and 5

=√(4×5)

=> √20 or

=> √(2×2×5)

=> 2√5

Finding the irrational number between 4 and √20:-

Let a = 4 and b =√20 then

The irrational number between 4 and √20

=√(4×√20)

=> √(√(4×4×20))

=>√√(320) or

=>√√(2×2×2×2×2×2×5)

=> 2√√(2×2×5)

=>2√√20

4 < √√320 < √20 < 5 or

4 < (320)^1/4 < (20)^1/2 < 5

Answer:-

The two irrational numbers between 4 and 5 are √20 or 2√5 and √√320 or 2√√20

Used formulae:-

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

• There are infinitely number of irrational numbers between any two numbers