Prove that root8 is irrational

1.	Prove that root8 is irrational
Answer» Let root 8be a rational no. So it can be written asRoot8=a/b {where a and b are co prime and rational}Squaring both side (root8) ^2=(a/b)^28=a^2 /b ^28b^2=a^2.....(1)Since 8 divides a^2, Then it divides a alsoFor some integer c8c=aPut the value of a=8c in equation (1)So,8b^2 = 64c^2B^2 =8cSince 8divides b^2Then it also divides bThat means a and b have 8 as common factor other than 1..that means a and b are not co-primeThis contradiction arises because of wrong assumption Hence root 8 is an irrational number.

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