[tex]a)\\ (\sqrt2}+\sqrt{8})^{2} = (\sqrt{2})^{2}+2\cdot\sqrt{2}\cdot\sqrt{8} + (\sqrt{8})^{2} =2+2\sqrt{2\cdot8} + 8 = 10+2\sqrt{16} =\\\\= 10+2\cdot4 =10+8 = 18[/tex]
[tex]b)\\(\sqrt{3}+2\sqrt{6})^{2} = (\sqrt{3})^{2}+2\cdot\sqrt{3}\cdot2\sqrt{6}+(2\sqrt{6})^{2} = 3 + 4\sqrt{3\cdot6}} +4\cdot 6 =3+4\sqrt{18}+24} =\\\\=27+4\sqrt{9\cdot2} = 27+4\cdot3\cdot\sqrt{2} = 27+12\sqrt{2}[/tex]
[tex]c)\\(\sqrt{10}-\sqrt{3})(\sqrt{10}+\sqrt{3})=(\sqrt{10})^{2}-(\sqrt{3})^{2} = 10-3 = 7[/tex]
Wykorzystano wzory skróconego mnożenia:
[tex](a+b)^{2} = a^{2}+2ab+b^{2}\\\\(a-b)(a+b) = a^{2}-b^{2}[/tex]
