Whakaoti i te 3sqrt{1-2/3+{left(1/2right)}^3}

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

Aromātai

$$\frac{\sqrt{66}}{4}\approx 2.031009601$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{3}{3}.

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

Tā te mea he rite te tauraro o \frac{3}{3} me \frac{2}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 2 i te 3, ka 1.

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

Tātaihia te \frac{1}{2} mā te pū o 3, kia riro ko \frac{1}{8}.

$$3\sqrt{\frac{1}{3}+\frac{1}{8}}$$

Ko te maha noa iti rawa atu o 3 me 8 ko 24. Me tahuri \frac{1}{3} me \frac{1}{8} ki te hautau me te tautūnga 24.

$$3\sqrt{\frac{8}{24}+\frac{3}{24}}$$

Tā te mea he rite te tauraro o \frac{8}{24} me \frac{3}{24}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$3\sqrt{\frac{8+3}{24}}$$

Tāpirihia te 8 ki te 3, ka 11.

$$3\sqrt{\frac{11}{24}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{11}{24}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{11}}{\sqrt{24}}.

$$3\times \frac{\sqrt{11}}{\sqrt{24}}$$

Tauwehea te 24=2^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 6} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{6}. Tuhia te pūtakerua o te 2^{2}.

$$3\times \frac{\sqrt{11}}{2\sqrt{6}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{11}}{2\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$3\times \frac{\sqrt{11}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$3\times \frac{\sqrt{11}\sqrt{6}}{2\times 6}$$

Hei whakarea \sqrt{11} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$3\times \frac{\sqrt{66}}{2\times 6}$$

Whakareatia te 2 ki te 6, ka 12.

$$3\times \frac{\sqrt{66}}{12}$$

Whakakorea atu te tauwehe pūnoa nui rawa 12 i roto i te 3 me te 12.

$$\frac{\sqrt{66}}{4}$$