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Give a proof that square root of n is irrational for every natural number n that is not a perfect square?
Wiki User
∙ 14y ago
Let's suppose the opposite and say that it is rational, so we can write it as a fraction of two natural numbers, where m <> 1:
l/m
Let's chose l and m in the way that the fraction l/m will be reduced, i.e, l and m have no common divider.
So, according to the supposed, (l/m)2 = n
From here, l2 = nm2
Now we see that l should be dividible by m. But we've chosen l and m in such a way that it couldn't be. Contradiction.
So we cannot represent the square of n as a rational fracture.
Wiki User
∙ 14y ago
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