Find an irrational number between <msqrt>

seiyakou2005n1

seiyakou2005n1

Answered question

2022-05-28

Find an irrational number between 2 and 3 .

Answer & Explanation

Julien Carrillo

Julien Carrillo

Beginner2022-05-29Added 13 answers

2 < 2 + 3 2 < 3
That is the Geometric Mean of 2 and 3 :
2 < ( 6 ) 1 4 < 3
It is easier to show that ( 6 ) 1 4 is irrational, rather than showing 2 2 + 3 2 is irrational
Monfredo0n

Monfredo0n

Beginner2022-05-30Added 6 answers

It can be π 2 . It is about 1.57, between 2 1.414 and 3 1.732.
Another one is the Golden Ratio ϕ = 1 + 5 2 1.618.

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