Prove that there is an irrational number between any two

garcialdaria2zky1

garcialdaria2zky1

Answered question

2022-05-15

Prove that there is an irrational number between any two unequal rational numbers a,b.

Answer & Explanation

heilaritikermx

heilaritikermx

Beginner2022-05-16Added 20 answers

2 is irrational. A rational times an irrational is irrational, and the sum of a rational with an irrational is irrational.
It's then easy to check that
s = a + 2 ( b a ) 2
is an irrational number between a and b.

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