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

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

Aromātai

$$1$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{3}}.

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

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{7}{3}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

Whakawehe \frac{\sqrt{15}}{3} ki te \frac{\sqrt{21}}{3} mā te whakarea \frac{\sqrt{15}}{3} ki te tau huripoki o \frac{\sqrt{21}}{3}.

$$\frac{\sqrt{15}\times 3}{3\sqrt{21}}\sqrt{\frac{7}{5}}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\sqrt{15}}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{15}}{\sqrt{21}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{21}.

$$\frac{\sqrt{15}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

Ko te pūrua o \sqrt{21} ko 21.

$$\frac{\sqrt{15}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Hei whakarea \sqrt{15} me \sqrt{21}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{315}}{21}\sqrt{\frac{7}{5}}$$

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}.

$$\frac{3\sqrt{35}}{21}\sqrt{\frac{7}{5}}$$

Whakawehea te 3\sqrt{35} ki te 21, kia riro ko \frac{1}{7}\sqrt{35}.

$$\frac{1}{7}\sqrt{35}\sqrt{\frac{7}{5}}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}}{\sqrt{5}}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{35}}{5}$$

Me whakarea te \frac{1}{7} ki te \frac{\sqrt{35}}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Whakareatia te 7 ki te 5, ka 35.

$$\frac{\sqrt{35}}{35}\sqrt{35}$$

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

$$\frac{\sqrt{35}\sqrt{35}}{35}$$

Whakareatia te \sqrt{35} ki te \sqrt{35}, ka 35.

$$\frac{35}{35}$$

Whakawehea te 35 ki te 35, kia riro ko 1.

$$1$$

Tauwehe

$$1$$