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Statement : There are infinitely many natural numbers n where the square root of n is rational.

Proof:

sqrt of n = x (where x is natural)

n= x squared

And n can be any natural number(x) squared ,and there are infinitely many natural numbers (x)

therefore there are infinitely many n which has a natural square root. Since natural numbers are rational , there are infinitely many natural numbers n where the square root of n is rational.