Proof: √5 is irrational

Step 1: Assume the opposite

Let us assume √5 is a rational number.

That means:

√5= a/b

a and b are integers,

b ≠ 0,

a and b have no common factor (they are coprime).

Conclusion:

Therefore, our assumption that √5 is rational is wrong.

Hence, √5 is irrational.

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