Question

show that 5+root 2 is not a rational number

Answer 1

let assume 5+root 2 is rational number
that is to find coprimes a and b(b#0) such that 5+root2=a/b
5=a/b- root 2
squaring on both sides
25=a^2/b^2+2-2.a/b.root2
2.a/b.root2=a^2/b^2+2-25
2.a/b.root2=a^2/b^2-23
=a^2-23b^2/b^2
root2 =a^2-23b^2/2ab
if a and b are integers root2 is rational
this contradicts the fact that root2 is irrational
Hence 5+root2 is irrational
So 5+root2 is not rational

Answer 2

Answer:

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