prove that √5 is an irrational number
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Let us assume the opposite, i.e., $\sqrt 5 $ is a rational number. Hence, $\sqrt 5 $ can be written as in the form $\dfrac{a}{b}$ where a and $b\;(b \ne 0)$ are co-prime (no common factor other than 1 ). By theorem: if $p$ is a prime number and $p$ divides ${a^2}$, then $p$ divides $a$, where a in a positive number.
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