a) [tex](\sqrt[]{2\frac{1}{4}}-\sqrt[]{\frac{9}{16}})\times1\frac{1}{3}\div3\frac{1}{3}=(\sqrt[]{\frac{9}{4}}-\frac{3}{4})\times\frac{4}{3}\div\frac{10}{3}=(\frac{3}{2}-\frac{3}{4})\times\frac{4}{3}\times\frac{3}{10}=\frac{3}{4}\times\frac{4}{3}\times\frac{3}{10}=1\times\frac{3}{10}=\frac{3}{10}=0,3[/tex]
b) [tex]4\frac{1}{2}(\sqrt[]{\frac{4}{9}}-\sqrt{\frac{1}{16}})\div1\frac{4}{5}=\frac{9}{2}\div(\frac{2}{3}-\frac{1}{4})\div\frac{9}{5}=\frac{9}{2}\div\frac{5}{12}\times\frac{5}{9}=\frac{9}{2}\times\frac{12}{5}\times\frac{5}{9}=\frac{1}{2}\times\frac{12}{5}\times5=\frac{1}{2}\times5=6[/tex]
c) [tex]\sqrt{1\frac{7}{9}} \div(2\frac{1}{4}-1\frac{5}{6})\div\sqrt{7\frac{1}{9}}=\sqrt{\frac{16}{9}}\div(\frac{9}{4}-\frac{11}{6})\div\sqrt{\frac{64}{9}}=\frac{4}{3}\div\frac{5}{12}\div\frac{8}{3}=\frac{4}{3}\times\frac{12}{5}\times\frac{3}{8}=4\times\frac{12}{5}\times\frac{1}{8}=\frac{12}{5}\times\frac{1}{2}=\frac{6}{5}=1,2[/tex]
Odpowiedź:
a) [tex](\sqrt[]{2\frac{1}{4}}-\sqrt[]{\frac{9}{16}})\times1\frac{1}{3}\div3\frac{1}{3}=(\sqrt[]{\frac{9}{4}}-\frac{3}{4})\times\frac{4}{3}\div\frac{10}{3}=(\frac{3}{2}-\frac{3}{4})\times\frac{4}{3}\times\frac{3}{10}=\frac{3}{4}\times\frac{4}{3}\times\frac{3}{10}=1\times\frac{3}{10}=\frac{3}{10}=0,3[/tex]
b) [tex]4\frac{1}{2}(\sqrt[]{\frac{4}{9}}-\sqrt{\frac{1}{16}})\div1\frac{4}{5}=\frac{9}{2}\div(\frac{2}{3}-\frac{1}{4})\div\frac{9}{5}=\frac{9}{2}\div\frac{5}{12}\times\frac{5}{9}=\frac{9}{2}\times\frac{12}{5}\times\frac{5}{9}=\frac{1}{2}\times\frac{12}{5}\times5=\frac{1}{2}\times5=6[/tex]
c) [tex]\sqrt{1\frac{7}{9}} \div(2\frac{1}{4}-1\frac{5}{6})\div\sqrt{7\frac{1}{9}}=\sqrt{\frac{16}{9}}\div(\frac{9}{4}-\frac{11}{6})\div\sqrt{\frac{64}{9}}=\frac{4}{3}\div\frac{5}{12}\div\frac{8}{3}=\frac{4}{3}\times\frac{12}{5}\times\frac{3}{8}=4\times\frac{12}{5}\times\frac{1}{8}=\frac{12}{5}\times\frac{1}{2}=\frac{6}{5}=1,2[/tex]