Question

Demonstrati ca √n este irational, cu n apartine Naturale fara 0,daca si numai daca in descompunerea in factori primi a lui n,cel putin un factor are exponentul impar

Answer 1

$\it \sqrt{a^{2k}} =a^k \in\mathbb{N}\\ \\ \sqrt{b^{2t+1}}=\sqrt{b^{2t}\cdot b}=b^t\sqrt{b} \notin\mathbb{Q}\\ \\ \sqrt{a^{2k}\cdot b^{2t+1}} =a^k\cdot b^t\sqrt{b} \notin\mathbb{Q}$