Whakaoti i te 5sqrt{11/3}3sqrt{54}

$$5 \sqrt{ 1 \frac{ 1 }{ 3 } } 3 \sqrt{ 54 }$$

Aromātai

$$90\sqrt{2}\approx 127.279220614$$

Ngā Upane Otinga

Whakareatia te 3 ki te 5, ka 15.

$$15\sqrt{\frac{1\times 3+1}{3}}\sqrt{54}$$

Whakareatia te 1 ki te 3, ka 3.

$$15\sqrt{\frac{3+1}{3}}\sqrt{54}$$

Tāpirihia te 3 ki te 1, ka 4.

$$15\sqrt{\frac{4}{3}}\sqrt{54}$$

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

$$15\times \frac{\sqrt{4}}{\sqrt{3}}\sqrt{54}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$15\times \frac{2}{\sqrt{3}}\sqrt{54}$$

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

$$15\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{54}$$

Ko te pūrua o \sqrt{3} ko 3.

$$15\times \frac{2\sqrt{3}}{3}\sqrt{54}$$

Tauwehea te 54=3^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 6} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{6}. Tuhia te pūtakerua o te 3^{2}.

$$15\times \frac{2\sqrt{3}}{3}\times 3\sqrt{6}$$

Whakareatia te 15 ki te 3, ka 45.

$$45\times \frac{2\sqrt{3}}{3}\sqrt{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 45 me te 3.

$$15\times 2\sqrt{3}\sqrt{6}$$

Whakareatia te 15 ki te 2, ka 30.

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

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}.

$$30\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$30\times 3\sqrt{2}$$

Whakareatia te 30 ki te 3, ka 90.

$$90\sqrt{2}$$