Question

prve √11 is a irrational no.
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Answer 1

Answer:

let√11 be rational.

then it must in the form of a / b [b is not equal to 0] [a and b are co-prime]

√11 = a / b

=> √11 x b = a

squaring on both sides

=> 11b^2 = a^2 ------> (1)

a^2 is divisible by 11

a is divisible by 11

a = 11c [c is a positive integer] [squaring on both sides ]

a^2 = 121 c^2 --------- > (2)

substitute a^2 in equ (1) we get

11b^2 = 121c^2

b^2 = 11c^2

=> b is divisible by 11

thus a and b have a common factor 11

there is a contradiction

as our assumption a & b are co prime but it has a common factor.

so √11 is an irrational.

Here is your answer....