Odpowiedź:
a) [tex]6 +4\sqrt{2}[/tex]
b) [tex]39 + 12\sqrt{3}[/tex]
c) 21 + [tex]4\sqrt{5}[/tex]
d) [tex]21 +12\sqrt{3}[/tex]
e) [tex]83+12\sqrt{35}[/tex]
f) [tex]98 + 40\sqrt{6}[/tex]
g) [tex]96+24\sqrt{12}[/tex]
h) [tex]188 +42\sqrt{20}[/tex]
Szczegółowe wyjaśnienie:
a) [tex](\sqrt{2} +2)^{2} = 2 + 4\sqrt{2} +4 = 6 +4\sqrt{2}[/tex]
b) [tex](6+\sqrt{3} )^{2} = 36 +12\sqrt{3} +3 = 39 + 12\sqrt{3}[/tex]
c) ([tex](2\sqrt{5} +1)^{2} = 20+4\sqrt{5} +1[/tex] = 21 + [tex]4\sqrt{5}[/tex]
d) [tex](3+2\sqrt{3} )^{2} = 9 +12\sqrt{3} +12 = 21 +12\sqrt{3}[/tex]
e) [tex](2\sqrt{5} +3\sqrt{7} )^{2} = 20+12\sqrt{35}+63 = 83+12\sqrt{35}[/tex]
f) [tex](4\sqrt{3} +5\sqrt{2} )^{2} = 48+40\sqrt{6} +50 = 98 + 40\sqrt{6}[/tex]
g) [tex](6\sqrt{2} +2\sqrt{6} )^{2}[/tex] = [tex]72+24\sqrt{12} +24 = 96+24\sqrt{12}[/tex]
h) [tex](7\sqrt{2} +3\sqrt{10} )^{2} = 98+42\sqrt{20} +90 = 188 +42\sqrt{20}[/tex]
