to show that√2 is irrational number
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Because √2 is not an integer (2 is not a perfect square), √2 must therefore be irrational. This proof can be generalized to show that any square root of any natural number that is not the square of a natural number is irrational.
If the number x solves some polynomial in the form of integers by positive powers of x, where the first term is a simple power of x, then x is either integer or irrational. So something like x²-n = 0 means that every sqrt(n) is irrational or integral.
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