12 a) [latex]sqrt{32}+sqrt{72}-sqrt{50}=4sqrt{2}+6sqrt{2}-5sqrt{2}=5sqrt{2}[/latex] b) [latex]sqrt{12}+sqrt{243}-sqrt{108}=2sqrt{3}+9sqrt{3}-6sqrt{3}=5sqrt{3}[/latex] c) [latex]sqrt{80}-sqrt{125}+sqrt{500}=4sqrt{5}-5sqrt{5}+10sqrt{5}=9sqrt{5}[/latex] d) [latex]sqrt{28}-sqrt{175}+sqrt{252}=2sqrt{7}-5sqrt{7} +6sqrt{7}=3sqrt{7}[/latex] e) [latex]sqrt{242}-sqrt{300}+sqrt{338}-sqrt{48}=\11sqrt{2}-10sqrt{3}+13sqrt{2}-4sqrt{3}=24sqrt{2}-14sqrt{3}[/latex] f) [latex]sqrt{800}+sqrt{80}-sqrt{200}+sqrt{500}=\20sqrt{2}+4sqrt{5}-10sqrt{2}+10sqrt{5}=10sqrt{2}+14sqrt{5}[/latex] g) [latex]sqrt{12}+sqrt{75}+sqrt{24}+sqrt{96}=\2sqrt{3}+5sqrt{3}+2sqrt{6}+4sqrt{6}=7sqrt{3}+6sqrt{6}[/latex] h) [latex]sqrt{392}-sqrt{150}+sqrt{578}-sqrt{486}=\14sqrt{2}-5sqrt{6}+17sqrt{2}-9sqrt{6}=31sqrt{2}-14sqrt{6}[/latex] ===================== 13 a) [latex]frac{2+4sqrt{5}}{2}=frac{2(1+2sqrt{5})}{2}=1+2sqrt{5}[/latex] b) [latex]frac{6-3sqrt{2}}{3}=frac{3(2-sqrt{2})}{3}=2-sqrt{2}[/latex] c) [latex]frac{-4+3sqrt{28}}{8}=frac{-4+3cdot 2sqrt{7}}{8}=\ frac{-4+6sqrt{7}}{8}=frac{2(-2+3sqrt{7})}{8}=frac{-2+3sqrt{7}}{4}[/latex] d) [latex]-frac{2+sqrt{8}}{2}=-frac{2+2sqrt{2}}{2}=\ -frac{2(1+sqrt{2})}{2}=-(1+sqrt{2})=-1-sqrt{2}[/latex] e) [latex]-frac{5-2sqrt{50}}{5}=-frac{5-2cdot 5sqrt{2}}{5}=\ -frac{5(1-2sqrt{2})}{5}=-(1-2sqrt{2})=-1+2sqrt{2}[/latex] f) [latex]frac{sqrt{12}-2sqrt{27}}{sqrt{3}}=frac{2sqrt{3}-2cdot 3sqrt{3}}{sqrt{3}}=\ frac{2sqrt{3}-6sqrt{3}}{sqrt{3}}=frac{-4sqrt{3}}{sqrt{3}}=-4[/latex] g) [latex]frac{sqrt{8}-4}{sqrt{2}-2}=frac{2sqrt{2}-4}{sqrt{2}-2}=frac{2(sqrt{2}-2)}{sqrt{2}-2}=2[/latex] h) [latex]frac{5+sqrt{6}}{sqrt{24}+10}=frac{5+sqrt{6}}{2sqrt{6}+10}=frac{5+sqrt{6}}{2(sqrt{6}+5)}=frac{1}{2}[/latex] ===================== 14 a) [latex]sqrt{2}cdotsqrt{6}-2sqrt{3}=sqrt{12}-2sqrt{3}=2sqrt{3}-2sqrt{3}=0[/latex] wymierna b) [latex](sqrt{5}-2)sqrt{5}+2sqrt{5}=5-2sqrt{5}+2sqrt{5}=5[/latex] wymierna c) [latex](2sqrt{2}-3)-(3+2sqrt{2})=2sqrt{2}-3-3-2sqrt{2}=-6[/latex] wymierna d) [latex]frac{3sqrt{2}-4sqrt{6}}{sqrt{2}}=frac{3sqrt{2}}{sqrt{2} } -frac{4sqrt{6}}{sqrt{2} }=3-4sqrt{3}[/latex] niewymierna e) [latex]5cdot (-2sqrt{3})+6sqrt{3}:2+4sqrt{3}=\ -10sqrt{3}+3sqrt{3}+4sqrt{3}=-3sqrt{3}[/latex] niewymierna f) [latex]frac{3sqrt{6}-3sqrt{2}}{sqrt{3}-1}=frac{3sqrt{2}(sqrt{3} -1)}{sqrt{3}-1}=3sqrt{2}[/latex] niewymierna g) [latex]frac{2sqrt{10}-2sqrt{2}}{2sqrt{2}}-sqrt{5}=frac{2sqrt{2}(sqrt{5}-1)}{2sqrt{2}}-sqrt{5}=\ sqrt{5}-1-sqrt{5}=-1[/latex] wymierna h) [latex]frac{4sqrt{15}-2sqrt{3}}{2sqrt{3}}+1=frac{4sqrt{15}}{2sqrt{3}} -frac{2sqrt{3}}{2sqrt{3}} +1=\ 2sqrt{5}-1+1=2sqrt{5}[/latex] niewymierna
