Question

√(5intreg si 5 pe 9) este un nr. rational sau irational?

Answer 1

$\sqrt{5\dfrac{5}{9}} = \sqrt{\dfrac{5\cdot 9+5}{9}} = \sqrt{\dfrac{45+5}{9}} = \sqrt{\dfrac{50}{9}}= \dfrac{\sqrt{50}}{\sqrt9} = \dfrac{\sqrt{5^2\cdot 2}}{3} = \dfrac{5\sqrt2}{3}\\ \\ \rightarrow \text{numarul de sub radical, adica 2, nu este patrat perfect }\Rightarrow \sqrt2\notin \mathbb_{Q} \\ \\ \\ \\ \Rightarrow \sqrt{5\dfrac{5}{9}} \notin \mathbb_{Q}\quad \text{(nu este numar rational, ci este irational)}$