Whakaoti i te sqrt{16/15:7/8-13/15:13/10+frac{1}{3}*frac{5}{3}}=

$$\sqrt { \frac { 16 } { 15 } : \frac { 7 } { 8 } - \frac { 13 } { 15 } : \frac { 13 } { 10 } + \frac { 1 } { 3 } \times \frac { 5 } { 3 } } =$$

Aromātai

$$\frac{\sqrt{12215}}{105}\approx 1.05258563$$

Ngā Upane Otinga

Whakawehe \frac{16}{15} ki te \frac{7}{8} mā te whakarea \frac{16}{15} ki te tau huripoki o \frac{7}{8}.

$$\sqrt{\frac{16}{15}\times \frac{8}{7}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

Me whakarea te \frac{16}{15} ki te \frac{8}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{16\times 8}{15\times 7}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{16\times 8}{15\times 7}.

$$\sqrt{\frac{128}{105}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

Whakawehe \frac{13}{15} ki te \frac{13}{10} mā te whakarea \frac{13}{15} ki te tau huripoki o \frac{13}{10}.

$$\sqrt{\frac{128}{105}-\frac{13}{15}\times \frac{10}{13}+\frac{1}{3}\times \frac{5}{3}}$$

Me whakarea te \frac{13}{15} ki te \frac{10}{13} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{128}{105}-\frac{13\times 10}{15\times 13}+\frac{1}{3}\times \frac{5}{3}}$$

Me whakakore tahi te 13 i te taurunga me te tauraro.

$$\sqrt{\frac{128}{105}-\frac{10}{15}+\frac{1}{3}\times \frac{5}{3}}$$

Whakahekea te hautanga \frac{10}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{128}{105}-\frac{2}{3}+\frac{1}{3}\times \frac{5}{3}}$$

Ko te maha noa iti rawa atu o 105 me 3 ko 105. Me tahuri \frac{128}{105} me \frac{2}{3} ki te hautau me te tautūnga 105.

$$\sqrt{\frac{128}{105}-\frac{70}{105}+\frac{1}{3}\times \frac{5}{3}}$$

Tā te mea he rite te tauraro o \frac{128}{105} me \frac{70}{105}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{128-70}{105}+\frac{1}{3}\times \frac{5}{3}}$$

Tangohia te 70 i te 128, ka 58.

$$\sqrt{\frac{58}{105}+\frac{1}{3}\times \frac{5}{3}}$$

Me whakarea te \frac{1}{3} ki te \frac{5}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{58}{105}+\frac{1\times 5}{3\times 3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 5}{3\times 3}.

$$\sqrt{\frac{58}{105}+\frac{5}{9}}$$

Ko te maha noa iti rawa atu o 105 me 9 ko 315. Me tahuri \frac{58}{105} me \frac{5}{9} ki te hautau me te tautūnga 315.

$$\sqrt{\frac{174}{315}+\frac{175}{315}}$$

Tā te mea he rite te tauraro o \frac{174}{315} me \frac{175}{315}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{174+175}{315}}$$

Tāpirihia te 174 ki te 175, ka 349.

$$\sqrt{\frac{349}{315}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{349}{315}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{349}}{\sqrt{315}}.

$$\frac{\sqrt{349}}{\sqrt{315}}$$

Tauwehea te 315=3^{2}\times 35. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 35} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{35}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\sqrt{349}}{3\sqrt{35}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{349}}{3\sqrt{35}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{35}.

$$\frac{\sqrt{349}\sqrt{35}}{3\left(\sqrt{35}\right)^{2}}$$

Ko te pūrua o \sqrt{35} ko 35.

$$\frac{\sqrt{349}\sqrt{35}}{3\times 35}$$

Hei whakarea \sqrt{349} me \sqrt{35}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{12215}}{3\times 35}$$

Whakareatia te 3 ki te 35, ka 105.

$$\frac{\sqrt{12215}}{105}$$