Zadanie 44.
a) [tex](\sqrt{10}+\sqrt{2})^2=10+2\sqrt{20}+2=12+2\sqrt{4*5}=12+2*2\sqrt5=12+4\sqrt5[/tex]
b) [tex](\sqrt{21}+\sqrt{3})^2=21+2\sqrt{63}+3=24+2\sqrt{9*7}=24+2*3\sqrt7=24+6\sqrt7[/tex]
c) [tex](\sqrt{15}-\sqrt{5})^2=15-2\sqrt{45}+5=20-2\sqrt{9*5}=20-2*3\sqrt5=20-6\sqrt5[/tex]
d) [tex](2\sqrt{2}-\sqrt{6})^2=8-4\sqrt{12}+6=14-4\sqrt{4*3}=14-4*2\sqrt3=14-8\sqrt3[/tex]
Zadanie 45.
a) [tex](\sqrt{21}-\sqrt{20})(\sqrt{21}+\sqrt{20})=21-20=1[/tex]
b) [tex]\sqrt{\sqrt{13}+2}*\sqrt{\sqrt{13}-2}=\sqrt{(\sqrt{13}+2)(\sqrt{13}-2)}=\sqrt{13-4}=\sqrt9=3[/tex]
c) [tex]\sqrt{5\sqrt{2}+7}*\sqrt{5\sqrt{2}-7}=\sqrt{(5\sqrt{2}+7)(5\sqrt{2}-7)}=\sqrt{50-49}=\sqrt1=1[/tex]
