Question

12 va rog neaparat !!!!!!

Answer 1

$\displaystyle a)~4\sqrt{3} =\sqrt{n} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0\\\\ 4\sqrt{3} =\sqrt{n} \Rightarrow \Big(4\sqrt{3} \Big)^2=\Big(\sqrt{n}\Big)^2 \Rightarrow 48=n \Rightarrow \boxed{n=48}$

$\displaystyle b)~5\sqrt{6} =\sqrt{n} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0\\\\ 5\sqrt{6} =\sqrt{n}\Rightarrow \Big(5\sqrt{6} \Big)^2=\Big(\sqrt{n}\Big)^2\Rightarrow 150=n \Rightarrow \boxed{n=150}$

$\displaystyle c)~7\sqrt{2} =\sqrt{n} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0\\\\ 7\sqrt{2} =\sqrt{n}\Rightarrow \Big(7\sqrt{2}\Big)^2=\Big(\sqrt{n}\Big)^2 \Rightarrow 98=n \Rightarrow \boxed{n=98}$

$\displaystyle d)~6\sqrt{10}=\sqrt{n}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0\\\\ 6\sqrt{10} =\sqrt{n}\Rightarrow \Big(6\sqrt{10} \Big)^2=\Big(\sqrt{n} \Big)^2 \Rightarrow 360=n \Rightarrow \boxed{n=360}$

$\displaystyle e)~3\sqrt{15} =\sqrt{n}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0 \\\\ 3\sqrt{15} =\sqrt{n} \Rightarrow \Big(3\sqrt{15}\Big)^2=\Big(\sqrt{n} \Big)^2 \Rightarrow 135=n \Rightarrow \boxed{n=135}$

$\displaystyle f)~2\sqrt{17} =\sqrt{n} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.:~~n\geq 0\\\\ 2\sqrt{17} =\sqrt{n} \Rightarrow \Big(2\sqrt{17}\Big)^2=\Big(\sqrt{n}\Big)^2 \Rightarrow 68=n \Rightarrow \boxed{n=68}$

Answer 2

Introducem factorii sub radical.

$\it a)\ \ \sqrt n=\sqrt{48} \Rightarrow n=48\\ \\ b)\ \ \sqrt n=\sqrt{150} \Rightarrow n=150\\ \\ c)\ \ \sqrt n=\sqrt{98} \Rightarrow n=98$

(continuă algoritmul)