Question

prove that √1/2(half) is an irrational number

Answer 1

let us assume 1/√2 as rational number
1/√2=a/b
(a,b are co primes,a,b€Z,HCF of a,b is1)
squaring on both sides
1/2=a^2/b^2
b^2=2a^2
2 divides b^2
2 also divides b
let b=2c
squaring on both sides
b^2=4c^2
2a^2=4c^2
a^2=2c^2
2 divides a^2
2 also divides a
2 is the common factor of a,b
but a,b are co primes
therefore it contridicts the hypothesis
so our assumption is wrong
1/√2 is irrational


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