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Verify by the method of contradiction `p : sqrt(11)` is irrational

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In this method, we assume that the given statement is false I.e.,`sqrt(11)` is irrational
So, there exists positive integer a and b such that `sqrt(11)=a/b` , where a and b have no common factors
`rArr11=a^2/b^2`
`rArra^2=11b^2`
So, 11 sivides `a^2` and also , 11 divides a
So, there exists an integer c such that
`a=11 c`
So, `a^2=121c^2`
`11b^2=121c^2`
`b^2=11c^2`
So, 11 divides `b^2`
also,11 divides b
So, 11 is the common factor of both a and b . this contradicts that a and b have no common factor. So, our earlier assumption that a and b have no common factor is wrong
So, " `sqrt(11)` is an irrational number " is true
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