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Exercise 1.2 * Proof that ##\sqrt{x}## isn't a rational number if ##x## isn't a perfect square (i.e. if ##x=n^2## for some ##n∈ℕ##).

In effect, if ##x=\frac{25}{9}##, so ##x## isn't a perfect square, then ##\sqrt{x}=\sqrt{\frac{25}{9}}=\frac{5}{3}## is rational.