solve root 2 is an irrational number

1.	solve root 2 is an irrational number
Answer» Let us assume that √2 is rational such that p and q are coprimes and q not equal to 0Therefore, √2 = p/q => √2q = p , SQUARING ON BOTH SIDES : 2q^2 = p^2 ,2 divides p^2 therefore 2 divides p__________(1)Let us take p = 2r for an integer rTherefore, => 2q^2 = (2r)^2=> q^2 = 2r^22 divides q^2 therefore it also divides q __________(2)From (1),(2) It shows that p and q have 2 as common factor, but it contradicts the fact that p and q are coprimes.This contradiction has arisen due to our wrong assumption.Therefore, we conclude that √2 is irrational //

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