Question

show that 2 + root 2 is not a rational number​

Answer 1

let we assume that 2+root 2 is an rational number
therefore there exist a unique pair of integers a and b which are co primes
such that
2+ root 2 = a/b
root 2 = a/b -2
root 2 = a-2b/b

here a-2b/b is a rational which is in the form of p/q
but root 2 is an irrational .
a rational cant be an irrational.
this contradiction arrises due to our wrong assumption that 2+root2 is rational is false hence it is an irrational .......


hence prooved

Answer 2

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