Question

(radical din 1152-radicaldin 1458)-(radical din512-radical648)rezolvare completa!!!!

Answer 1

[tex]1152=12^2\cdot2^3\Leftrightarrow \sqrt{1152}=\sqrt{12^2\cdot2^3}=12\cdot2^2\sqrt{2}=48\sqrt{2}\\ 1485=2\cdot3^6\Leftrightarrow \sqrt{1485}=\sqrt{2\cdot3^6}=3^3\sqrt{2}=27\sqrt{2}\\ 512=2^9\Leftrightarrow \sqrt{512}=\sqrt{2^9}=2^4\sqrt{2}=16\sqrt{2}\\ 648=2^3\cdot3^4\Leftrightarrow \sqrt{648}=\sqrt{3^4\cdot2^3}=3^2\cdot2^2\sqrt{2}=36\sqrt{2}[/tex]
Deci 
$(\sqrt{1152}-\sqrt{1458})-(\sqrt{512}-\sqrt{648})=48\sqrt{2}-27\sqrt{2}-16\sqrt{2}+36\sqrt{2}\\ =41\sqrt{2}$