Przykład A
[tex]\sqrt{8}\cdot(3\sqrt{8} -\sqrt{2} ) =3\sqrt{64} -\sqrt{16}=3\cdot8-4=24-4=\boxed{20}[/tex]
Przykład B
[tex](4-\sqrt{2})(1+3\sqrt{3} )(4+\sqrt{2})=[4^2-(\sqrt{2})^2](1+3\sqrt{3})=\\\\(16-2)(1+3\sqrt{3})=12\cdot(1+3\sqrt{3})=\boxed{12+36\sqrt{3}}[/tex]
Przykład C
[tex][(\sqrt{3}-1)(2\sqrt{3}+5)]^2=[\sqrt{3}\cdot2\sqrt{3}+5\sqrt{3}-2\sqrt{3}-5]^2=\\\\(3\cdot2+3\sqrt{3}-5)^2= (6-5+3\sqrt{3})^2 =(1-3\sqrt{3})^2 =\\\\1^2+(3\sqrt{3})^2-2\cdot1\cdot3\sqrt{3}=1+9\cdot3-6\sqrt{3} =\boxed{28-6\sqrt{3}}[/tex]
