Question

prove that root 2 is irrational

Answer 1

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Answer 2

Let us assume that root2 is rational.
root2=a/b where a nd b are coprime.
broot2=a

squaring on both sides,
2b^2=a^2
therefore 2divide a square
therefore 2divide a
a=2c for some integer c.
substituting for a we get 2b^2=4c^2
This means that 2 divide b square and also to divide b.
therefore a and b have at least 2 as Common Factor.
But this contradicts the fact that a and b have no common factors other than 1.
This contradiction has arisen because of our incorrect assumption that root 2 is rational.
So,root2 is irrational.