Q. 53.8( 10 Votes )

Which of the foll

Answer :

Proof: let us assume that √7 be rational.

then it must in the form of p / q [q ≠ 0] [p and q are co-prime]


√7 = p / q


√7 x q = p


squaring on both sides


7q2= p2 (i)


p2 is divisible by 7


p is divisible by 7


p = 7c [c is a positive integer] [squaring on both sides ]


p2 = 49 c2 (ii)


Substitute p2 in eq (i), we get,


7q2 = 49 c2


q2 = 7c2


q is divisible by 7


Thus q and p have a common factor 7.


There is a contradiction


As our assumption p & q are co - prime but it has a common factor.


So that √7 is an irrational.

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