Răspuns:
41√6
Explicație pas cu pas:
[tex]\sqrt{27} (\sqrt{32} -\sqrt{72} +\sqrt{162} -\sqrt{288} )-\sqrt{8} (2\sqrt{108} -5\sqrt{192} )=[/tex]
[tex]=\sqrt{9*3} (\sqrt{16*2} -\sqrt{36*2} +\sqrt{81*2} -\sqrt{144*2} )-\sqrt{4*2} (2\sqrt{36*3} -5\sqrt{64*3} )=[/tex]
[tex]=3\sqrt{3} (4\sqrt{2} -6\sqrt{2} +9\sqrt{2} -12\sqrt{2} )-2\sqrt{2} (12\sqrt{3} -40\sqrt{3} )=[/tex]
[tex]=3\sqrt{3} (-5\sqrt{2} )-2\sqrt{2} (-28\sqrt{3} )=[/tex]
[tex]=-15\sqrt{6}+56\sqrt{6} =[/tex]
[tex]=41\sqrt{6}[/tex]
