Whakaoti i te sqrt{{2/3+5/4:[1+3/4*(1/3+frac{1}{4}*frac{12}{7})-frac{1}{7}]}*frac{3}{37}+frac{1}{64}}

$$\sqrt { \{ \frac { 2 } { 3 } + \frac { 5 } { 4 } : [ 1 + \frac { 3 } { 4 } \times ( \frac { 1 } { 3 } + \frac { 1 } { 4 } \times \frac { 12 } { 7 } ) - \frac { 1 } { 7 } ] \} \times \frac { 3 } { 37 } + \frac { 1 } { 64 } }$$

Aromātai

$$\frac{3}{8}=0.375$$

Ngā Upane Otinga

Me whakarea te \frac{1}{4} ki te \frac{12}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\left(\frac{1}{3}+\frac{1\times 12}{4\times 7}\right)-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 12}{4\times 7}.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\left(\frac{1}{3}+\frac{12}{28}\right)-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Whakahekea te hautanga \frac{12}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\left(\frac{1}{3}+\frac{3}{7}\right)-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Ko te maha noa iti rawa atu o 3 me 7 ko 21. Me tahuri \frac{1}{3} me \frac{3}{7} ki te hautau me te tautūnga 21.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\left(\frac{7}{21}+\frac{9}{21}\right)-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tā te mea he rite te tauraro o \frac{7}{21} me \frac{9}{21}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\times \frac{7+9}{21}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tāpirihia te 7 ki te 9, ka 16.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3}{4}\times \frac{16}{21}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Me whakarea te \frac{3}{4} ki te \frac{16}{21} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{3\times 16}{4\times 21}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 16}{4\times 21}.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{48}{84}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Whakahekea te hautanga \frac{48}{84} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{1+\frac{4}{7}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Me tahuri te 1 ki te hautau \frac{7}{7}.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{\frac{7}{7}+\frac{4}{7}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tā te mea he rite te tauraro o \frac{7}{7} me \frac{4}{7}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{\frac{7+4}{7}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tāpirihia te 7 ki te 4, ka 11.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{\frac{11}{7}-\frac{1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tā te mea he rite te tauraro o \frac{11}{7} me \frac{1}{7}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{\frac{11-1}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tangohia te 1 i te 11, ka 10.

$$\sqrt{\left(\frac{2}{3}+\frac{\frac{5}{4}}{\frac{10}{7}}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Whakawehe \frac{5}{4} ki te \frac{10}{7} mā te whakarea \frac{5}{4} ki te tau huripoki o \frac{10}{7}.

$$\sqrt{\left(\frac{2}{3}+\frac{5}{4}\times \frac{7}{10}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Me whakarea te \frac{5}{4} ki te \frac{7}{10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\left(\frac{2}{3}+\frac{5\times 7}{4\times 10}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 7}{4\times 10}.

$$\sqrt{\left(\frac{2}{3}+\frac{35}{40}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Whakahekea te hautanga \frac{35}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\left(\frac{2}{3}+\frac{7}{8}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Ko te maha noa iti rawa atu o 3 me 8 ko 24. Me tahuri \frac{2}{3} me \frac{7}{8} ki te hautau me te tautūnga 24.

$$\sqrt{\left(\frac{16}{24}+\frac{21}{24}\right)\times \frac{3}{37}+\frac{1}{64}}$$

Tā te mea he rite te tauraro o \frac{16}{24} me \frac{21}{24}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{16+21}{24}\times \frac{3}{37}+\frac{1}{64}}$$

Tāpirihia te 16 ki te 21, ka 37.

$$\sqrt{\frac{37}{24}\times \frac{3}{37}+\frac{1}{64}}$$

Me whakarea te \frac{37}{24} ki te \frac{3}{37} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{37\times 3}{24\times 37}+\frac{1}{64}}$$

Me whakakore tahi te 37 i te taurunga me te tauraro.

$$\sqrt{\frac{3}{24}+\frac{1}{64}}$$

Whakahekea te hautanga \frac{3}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{1}{8}+\frac{1}{64}}$$

Ko te maha noa iti rawa atu o 8 me 64 ko 64. Me tahuri \frac{1}{8} me \frac{1}{64} ki te hautau me te tautūnga 64.

$$\sqrt{\frac{8}{64}+\frac{1}{64}}$$

Tā te mea he rite te tauraro o \frac{8}{64} me \frac{1}{64}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{8+1}{64}}$$

Tāpirihia te 8 ki te 1, ka 9.

$$\sqrt{\frac{9}{64}}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{9}{64} hei whakawehenga o ngā pūtake rua \frac{\sqrt{9}}{\sqrt{64}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{3}{8}$$

Tauwehe

$$\frac{3}{2 ^ {3}} = 0.375$$