show that √5 is irrational
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Let's assume that √5 is a rational number. If √5 is rational, that means it can be written in the form of a/b, where a and b integers that have no common factor other than 1 and b ≠ 0. This means 5 divides a². ... So, we conclude that √5 is irrational.
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If √5 is rational, that means it can be written in the form of a/b, where a and b integers that have no common factor other than 1 and b ≠ 0. This means 5 divides a². That means it also divides a. ... So, we conclude that √5 is irrational.
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