Whakaoti i te sqrt{{[(3/5+1/10):7/20-(6/5+frac{7}{2}-frac{14}{5})]:frac{2}{3}-frac{1}{15}}:(frac{2}{3})^2}

$$\sqrt { \{ [ ( \frac { 3 } { 5 } + \frac { 1 } { 10 } ) : \frac { 7 } { 20 } - ( \frac { 6 } { 5 } + \frac { 7 } { 2 } - \frac { 14 } { 5 } ) ] : \frac { 2 } { 3 } - \frac { 1 } { 15 } \} : ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Aromātai

$$\frac{\sqrt{3}}{4}\approx 0.433012702$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 5 me 10 ko 10. Me tahuri \frac{3}{5} me \frac{1}{10} ki te hautau me te tautūnga 10.

$$\sqrt{\frac{\frac{\frac{\frac{6}{10}+\frac{1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tā te mea he rite te tauraro o \frac{6}{10} me \frac{1}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{\frac{\frac{\frac{6+1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\sqrt{\frac{\frac{\frac{\frac{7}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Whakawehe \frac{7}{10} ki te \frac{7}{20} mā te whakarea \frac{7}{10} ki te tau huripoki o \frac{7}{20}.

$$\sqrt{\frac{\frac{\frac{7}{10}\times \frac{20}{7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Me whakarea te \frac{7}{10} ki te \frac{20}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{\frac{\frac{7\times 20}{10\times 7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

$$\sqrt{\frac{\frac{\frac{20}{10}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Whakawehea te 20 ki te 10, kia riro ko 2.

$$\sqrt{\frac{\frac{2-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Ko te maha noa iti rawa atu o 5 me 2 ko 10. Me tahuri \frac{6}{5} me \frac{7}{2} ki te hautau me te tautūnga 10.

$$\sqrt{\frac{\frac{2-\left(\frac{12}{10}+\frac{35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tā te mea he rite te tauraro o \frac{12}{10} me \frac{35}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{\frac{2-\left(\frac{12+35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tāpirihia te 12 ki te 35, ka 47.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Ko te maha noa iti rawa atu o 10 me 5 ko 10. Me tahuri \frac{47}{10} me \frac{14}{5} ki te hautau me te tautūnga 10.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{28}{10}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tā te mea he rite te tauraro o \frac{47}{10} me \frac{28}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{\frac{2-\frac{47-28}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tangohia te 28 i te 47, ka 19.

$$\sqrt{\frac{\frac{2-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Me tahuri te 2 ki te hautau \frac{20}{10}.

$$\sqrt{\frac{\frac{\frac{20}{10}-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tā te mea he rite te tauraro o \frac{20}{10} me \frac{19}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{\frac{\frac{20-19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Tangohia te 19 i te 20, ka 1.

$$\sqrt{\frac{\frac{\frac{1}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Whakawehe \frac{1}{10} ki te \frac{2}{3} mā te whakarea \frac{1}{10} ki te tau huripoki o \frac{2}{3}.

$$\sqrt{\frac{\frac{1}{10}\times \frac{3}{2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Me whakarea te \frac{1}{10} ki te \frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{\frac{1\times 3}{10\times 2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{10\times 2}.

$$\sqrt{\frac{\frac{3}{20}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Ko te maha noa iti rawa atu o 20 me 15 ko 60. Me tahuri \frac{3}{20} me \frac{1}{15} ki te hautau me te tautūnga 60.

$$\sqrt{\frac{\frac{9}{60}-\frac{4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Tā te mea he rite te tauraro o \frac{9}{60} me \frac{4}{60}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{\frac{9-4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Tangohia te 4 i te 9, ka 5.

$$\sqrt{\frac{\frac{5}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Whakahekea te hautanga \frac{5}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{\frac{1}{12}}{\left(\frac{2}{3}\right)^{2}}}$$

Tātaihia te \frac{2}{3} mā te pū o 2, kia riro ko \frac{4}{9}.

$$\sqrt{\frac{\frac{1}{12}}{\frac{4}{9}}}$$

Whakawehe \frac{1}{12} ki te \frac{4}{9} mā te whakarea \frac{1}{12} ki te tau huripoki o \frac{4}{9}.

$$\sqrt{\frac{1}{12}\times \frac{9}{4}}$$

Me whakarea te \frac{1}{12} ki te \frac{9}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{1\times 9}{12\times 4}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 9}{12\times 4}.

$$\sqrt{\frac{9}{48}}$$

Whakahekea te hautanga \frac{9}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{3}{16}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{16}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{16}}.

$$\frac{\sqrt{3}}{\sqrt{16}}$$

Tātaitia te pūtakerua o 16 kia tae ki 4.

$$\frac{\sqrt{3}}{4}$$