a) [latex]sqrt{242}-sqrt{300}+sqrt{338}-sqrt{48}=\\sqrt{121*2}-sqrt{100*3}+sqrt{169*2}-sqrt{16*3}=\\11sqrt{2}-10sqrt{3}+13sqrt{2}-4sqrt{3}=24sqrt{2}-14sqrt{3} [/latex] b) [latex]sqrt{12}+sqrt{75}+sqrt{24}+sqrt{96}=sqrt{4*3}+sqrt{25*3}+sqrt{4*6}+sqrt{16*6}=\\2sqrt{3}+5sqrt{3}+2sqrt{6}+4sqrt{6}=7sqrt{3}+6sqrt{6} [/latex]
[latex] sqrt{242} - sqrt{300} + sqrt{338} - sqrt{48} =\= sqrt{121*2} - sqrt{100*3} + sqrt{169*2}- sqrt{16*3} =\= sqrt{121} * sqrt{2} - sqrt{100} * sqrt{3} + sqrt{169} * sqrt{2} - sqrt{16} * sqrt{3} =\=11* sqrt{2} -10* sqrt{3} +13* sqrt{2} -4* sqrt{3} =\=11 sqrt{2} -10 sqrt{3} +13 sqrt{2} -4 sqrt{3} =\=24 sqrt{2} -14 sqrt{3}[/latex] [latex]sqrt{12} + sqrt{75} + sqrt{24} + sqrt{96} =\= sqrt{4*3} + sqrt{25*3} + sqrt{4*6} + sqrt{16*6} =\= sqrt{4} * sqrt{3} + sqrt{25} * sqrt{3} + sqrt{4} * sqrt{6} + sqrt{16} * sqrt{6} =\=2* sqrt{3} +5* sqrt{3} +2 *sqrt{6} +4* sqrt{6} =\=2 sqrt{3} +5 sqrt{3} +2 sqrt{6} +4 sqrt{6} =\=7 sqrt{3} +6 sqrt{6} [/latex]
