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Question

Show that 32 is irrational.


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Solution

Let us assume, to the contrary, that 32 is rational.
That is, we can find coprime a and b (b 0) such that 32 = ab
Rearranging, we get 2 = a3b
Since 3, a and b are integers, a3b is rational, and so 2 is rational.
But this contradicts the fact that 2 is irrational.
So, we conclude that 32 is irrational.


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