Math CentralQuandaries & Queries


Subject: Discrete Mathematics
Name: Humera
Who are you: Student
Prove that square root of 3 is irrational.


Start by assuming the opposite (that it is rational). Then there exist two integers a and b, whose greatest common divisor (GCD) is 1, such that a/b is the square root of three. That's what rational means.

Using this assumption, you should be able to show that both a and b are multiples of 3 and that means the GCD is at least 3, which is a contradiction of your assumption, meaning that square root of 3 is not rational.

Hope this helps,
Stephen La Rocque.

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