Whakaoti i te 2sqrt{3}divsqrt{7/3}*sqrt{7/5}

$$2 \sqrt{ 3 } \div \sqrt{ \frac{ 7 }{ 3 } } \times \sqrt{ \frac{ 7 }{ 5 } }$$

Aromātai

$$\frac{6\sqrt{5}}{5}\approx 2.683281573$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{7}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{7}}{\sqrt{3}}.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{7}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2\sqrt{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

Whakawehe 2\sqrt{3} ki te \frac{\sqrt{21}}{3} mā te whakarea 2\sqrt{3} ki te tau huripoki o \frac{\sqrt{21}}{3}.

$$\frac{2\sqrt{3}\times 3}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{3}\times 3}{\sqrt{21}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{21}.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

Ko te pūrua o \sqrt{21} ko 21.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{6\sqrt{3}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Tauwehea te 21=3\times 7. Tuhia anō te pūtake rua o te hua \sqrt{3\times 7} hei hua o ngā pūtake rua \sqrt{3}\sqrt{7}.

$$\frac{6\sqrt{3}\sqrt{3}\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

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

$$\frac{6\times 3\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{18\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Whakawehea te 18\sqrt{7} ki te 21, kia riro ko \frac{6}{7}\sqrt{7}.

$$\frac{6}{7}\sqrt{7}\sqrt{\frac{7}{5}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{7}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{7}}{\sqrt{5}}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}}{\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{7}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

Hei whakarea \sqrt{7} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{35}}{5}$$

Me whakarea te \frac{6}{7} ki te \frac{\sqrt{35}}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{6\sqrt{35}}{7\times 5}\sqrt{7}$$

Whakareatia te 7 ki te 5, ka 35.

$$\frac{6\sqrt{35}}{35}\sqrt{7}$$

Tuhia te \frac{6\sqrt{35}}{35}\sqrt{7} hei hautanga kotahi.

$$\frac{6\sqrt{35}\sqrt{7}}{35}$$

Tauwehea te 35=7\times 5. Tuhia anō te pūtake rua o te hua \sqrt{7\times 5} hei hua o ngā pūtake rua \sqrt{7}\sqrt{5}.

$$\frac{6\sqrt{7}\sqrt{5}\sqrt{7}}{35}$$

Whakareatia te \sqrt{7} ki te \sqrt{7}, ka 7.

$$\frac{6\times 7\sqrt{5}}{35}$$

Whakareatia te 6 ki te 7, ka 42.

$$\frac{42\sqrt{5}}{35}$$

Whakawehea te 42\sqrt{5} ki te 35, kia riro ko \frac{6}{5}\sqrt{5}.

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