Question

Dați exemple de numere raționale cuprinse între:
$a \: )\sqrt{12} si \sqrt{13}$
$b) - \sqrt{15} si - \sqrt{14}$

Vă rog!​

Answer 1

$a)\quad 35^2 = 1225 \\ \\ 12 < 12,25 < 13 \\\\ \Leftrightarrow\,\sqrt{12}<\sqrt{12,25}<\sqrt{13}\\\\ \Leftrightarrow\,\sqrt{12}<\boxed{3,5} <\sqrt{13}\\\\36^2 = 1296 \Rightarrow \sqrt{12} <\boxed{3,6} < \sqrt{13}$

$b)\quad 38^2 = 1444\\ \\ 14 < 14,44<15\\ \\ \Leftrightarrow\,\sqrt{14}<\sqrt{14,44}<\sqrt{15} \\\\\Leftrightarrow\,\sqrt{14}<3,8<\sqrt{15}\\ \\ \Leftrightarrow \, -\sqrt{15}<\boxed{-3,8}<-\sqrt{14}\\ \\38,1^2 = 1451,61\Rightarrow -\sqrt{15}<\boxed{-3,81}<-\sqrt{14}$