Odpowiedź:
[tex]a)\ \ (1-\sqrt{3})^2=1^2-2\cdot1\cdot\sqrt{3}+(\sqrt{3})^2=1-2\sqrt{3}+3=4-2\sqrt{3}\\\\\\b)\ \ (3-\sqrt{5})^2=3^2-2\cdot3\cdot\sqrt{5}+(\sqrt{5})^2=9-6\sqrt{5}+5=14-6\sqrt{5}\\\\\\c)\ \ (\sqrt{2}-4)^2=(\sqrt{2})^2-2\sqrt{2}\cdot4+4^2=2-8\sqrt{2}+16=18-8\sqrt{2}\\\\\\d)\ \ (\sqrt{7}-5)^2=(\sqrt{7})^2-2\sqrt{7}\cdot5+5^2=7-10\sqrt{7}+25=32-10\sqrt{7}\\\\\\e)\ \ (\sqrt{2}-\sqrt{3})^2=(\sqrt{2})^2-2\sqrt{2}\cdot\sqrt{3}+(\sqrt{3})^2=2-2\sqrt{6}+3=5-2\sqrt{6}\\\\\\ [/tex]
[tex]f)\ \ (2\sqrt{2}-3\sqrt{3})^2=(2\sqrt{2})^2-2\cdot2\sqrt{2}\cdot3\sqrt{3}+(3\sqrt{3})^2=4\cdot2-4\sqrt{2}\cdot3\sqrt{3}+9\cdot3=\\\\=8-12\sqrt{6}+27=35-12\sqrt{6}\\\\\\g)\ \ (3\sqrt{5}-4\sqrt{6})^2=(3\sqrt{5})^2-2\cdot3\sqrt{5}\cdot4\sqrt{6}+(4\sqrt{6})^2=9\cdot5-6\sqrt{5}\cdot4\sqrt{6}+16\cdot6=\\\\=45-24\sqrt{30}+96=141-24\sqrt{30} [/tex]
[tex]h)\ \ (2\sqrt{10}-5\sqrt{2})^2=(2\sqrt{10})^2-2\cdot2\sqrt{10}\cdot5\sqrt{2}+(5\sqrt{2})^2=\\\\=4\cdot10-4\sqrt{10}\cdot5\sqrt{2}+25\cdot2=40-20\sqrt{20}+50=90-20\sqrt{20}=\\\\=90-20\sqrt{4\cdot5}=90-20\cdot2\sqrt{5}=90-40\sqrt{5} [/tex]
