Root 2 is an irrational Number -
Let us assume, to the contrary, that root 2 is rational.
So, we can find integers r and s(≠0) such that 2=
Suppose rand shave a common factor other than 1. Then, we divide by the common factor to get , 2
= where a and bare coprime.
So, b 2= a.
Squaring on both sides and rearranging, we get 2b
. Therefore, 2 divides a
it follows that 2 divides a.
So, we can write a= 2c for some integer c.
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