Whakaoti i te sqrt{4/3}divsqrt{8/3}*sqrt{8/5}

$$\sqrt { \frac { 4 } { 3 } } \div \sqrt { \frac { 8 } { 3 } } \times \sqrt { \frac { 8 } { 5 } }$$

Aromātai

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{4}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{4}}{\sqrt{3}}}{\sqrt{\frac{8}{3}}}\sqrt{\frac{8}{5}}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{\frac{2}{\sqrt{3}}}{\sqrt{\frac{8}{3}}}\sqrt{\frac{8}{5}}$$

Whakangāwaritia te tauraro o \frac{2}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{8}{3}}}\sqrt{\frac{8}{5}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{2\sqrt{3}}{3}}{\sqrt{\frac{8}{3}}}\sqrt{\frac{8}{5}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{\sqrt{8}}{\sqrt{3}}}\sqrt{\frac{8}{5}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{2\sqrt{2}}{\sqrt{3}}}\sqrt{\frac{8}{5}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{2}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{8}{5}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{2\sqrt{2}\sqrt{3}}{3}}\sqrt{\frac{8}{5}}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{2\sqrt{6}}{3}}\sqrt{\frac{8}{5}}$$

Whakawehe \frac{2\sqrt{3}}{3} ki te \frac{2\sqrt{6}}{3} mā te whakarea \frac{2\sqrt{3}}{3} ki te tau huripoki o \frac{2\sqrt{6}}{3}.

$$\frac{2\sqrt{3}\times 3}{3\times 2\sqrt{6}}\sqrt{\frac{8}{5}}$$

Me whakakore tahi te 2\times 3 i te taurunga me te tauraro.

$$\frac{\sqrt{3}}{\sqrt{6}}\sqrt{\frac{8}{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{3}}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\sqrt{\frac{8}{5}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\sqrt{3}\sqrt{6}}{6}\sqrt{\frac{8}{5}}$$

Tauwehea te 6=3\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3\times 2} hei hua o ngā pūtake rua \sqrt{3}\sqrt{2}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{2}}{6}\sqrt{\frac{8}{5}}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{3\sqrt{2}}{6}\sqrt{\frac{8}{5}}$$

Whakawehea te 3\sqrt{2} ki te 6, kia riro ko \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}\sqrt{\frac{8}{5}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{1}{2}\sqrt{2}\times \frac{\sqrt{8}}{\sqrt{5}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{1}{2}\sqrt{2}\times \frac{2\sqrt{2}}{\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{2}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{1}{2}\sqrt{2}\times \frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{1}{2}\sqrt{2}\times \frac{2\sqrt{2}\sqrt{5}}{5}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{1}{2}\sqrt{2}\times \frac{2\sqrt{10}}{5}$$

Me whakarea te \frac{1}{2} ki te \frac{2\sqrt{10}}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2\sqrt{10}}{2\times 5}\sqrt{2}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{\sqrt{10}}{5}\sqrt{2}$$

Tuhia te \frac{\sqrt{10}}{5}\sqrt{2} hei hautanga kotahi.

$$\frac{\sqrt{10}\sqrt{2}}{5}$$

Tauwehea te 10=2\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2\times 5} hei hua o ngā pūtake rua \sqrt{2}\sqrt{5}.

$$\frac{\sqrt{2}\sqrt{5}\sqrt{2}}{5}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{2\sqrt{5}}{5}$$