a)
[tex]2\sqrt{50}-3\sqrt{18}+0,35\sqrt{200}=\\\\=2\sqrt{25\cdot2}-3\sqrt{9\cdot2}+0,35\sqrt{100\cdot2}=\\\\=2\sqrt{5^2\cdot2}-3\sqrt{3^2\cdot2}+0,35\sqrt{10^2\cdot2}=\\\\=2\cdot5\sqrt2-3\cdot3\sqrt2+0,35\cdot10\sqrt2=\\\\=10\sqrt2-9\sqrt2+3,5\sqrt2=\sqrt2+3,5\sqrt2=\boxed{4,5\sqrt2}[/tex]
b)
[tex](6-3\sqrt2)(6+3\sqrt2)=6^2-(3\sqrt2)^2=\\\\=36-3^2\cdot(\sqrt2)^2=36-9\cdot2=\\\\=36-18=\boxed{18}[/tex]
Wykorzystany wzór skróconego mnożenia
[tex](a+b)(a-b)=a^2-b^2[/tex]
