Whakaoti i te sqrt{1frac{2/3}}{sqrt{5/6}}

$$\frac{ \sqrt{ 1 \frac{ 2 }{ 3 } } }{ \sqrt{ \frac{ 5 }{ 6 } } }$$

Aromātai

$$\sqrt{2}\approx 1.414213562$$

Ngā Upane Otinga

Whakareatia te 1 ki te 3, ka 3.

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

Tāpirihia te 3 ki te 2, ka 5.

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

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

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

$$\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{5}{6}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{6}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{\sqrt{6}}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{6}}$$

Hei whakarea \sqrt{5} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{6}}$$

Whakawehe \frac{\sqrt{15}}{3} ki te \frac{\sqrt{30}}{6} mā te whakarea \frac{\sqrt{15}}{3} ki te tau huripoki o \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{15}\times 6}{3\sqrt{30}}$$

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

$$\frac{2\sqrt{15}}{\sqrt{30}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{15}}{\sqrt{30}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{30}.

$$\frac{2\sqrt{15}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

Ko te pūrua o \sqrt{30} ko 30.

$$\frac{2\sqrt{15}\sqrt{30}}{30}$$

Tauwehea te 30=15\times 2. Tuhia anō te pūtake rua o te hua \sqrt{15\times 2} hei hua o ngā pūtake rua \sqrt{15}\sqrt{2}.

$$\frac{2\sqrt{15}\sqrt{15}\sqrt{2}}{30}$$

Whakareatia te \sqrt{15} ki te \sqrt{15}, ka 15.

$$\frac{2\times 15\sqrt{2}}{30}$$

Whakareatia te 2 ki te 15, ka 30.

$$\frac{30\sqrt{2}}{30}$$

Me whakakore te 30 me te 30.

$$\sqrt{2}$$