Question

Represent the following irrational √11​

Answer 1

Step-by-step explanation:

Sol: let√11 be rational. then it must in the form of p / q [q is not equal to 0] [p and q are co-prime]

√11 = p / q => √11 x q = p squaring on both sides => 11q2= p2 ------> (1) p2 is divisible by 11 p is divisible by 11 p = 11c [c is a positive integer] [squaring on both sides ] p2 = 121 c2 --------- > (2) subsitute p2 in equ (1) we get 11q2 = 121c2 q2 = 11c2 => q is divisble by 11 thus q and p have a common factor 11 there is a contradiction as our assumsion p & q are co prime but it has a common factor. so √11 is an irrational

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