Whakaoti i te sqrt{832*468/21*1001}

$$\sqrt { \frac { 832 \times 468 } { 21 \times 1001 } }$$

Aromātai

$$\frac{16\sqrt{429}}{77}\approx 4.303857699$$

Ngā Upane Otinga

Me whakakore tahi te 3\times 13 i te taurunga me te tauraro.

$$\sqrt{\frac{64\times 156}{7\times 77}}$$

Whakareatia te 64 ki te 156, ka 9984.

$$\sqrt{\frac{9984}{7\times 77}}$$

Whakareatia te 7 ki te 77, ka 539.

$$\sqrt{\frac{9984}{539}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{9984}{539}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{9984}}{\sqrt{539}}.

$$\frac{\sqrt{9984}}{\sqrt{539}}$$

Tauwehea te 9984=16^{2}\times 39. Tuhia anō te pūtake rua o te hua \sqrt{16^{2}\times 39} hei hua o ngā pūtake rua \sqrt{16^{2}}\sqrt{39}. Tuhia te pūtakerua o te 16^{2}.

$$\frac{16\sqrt{39}}{\sqrt{539}}$$

Tauwehea te 539=7^{2}\times 11. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 11} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{11}. Tuhia te pūtakerua o te 7^{2}.

$$\frac{16\sqrt{39}}{7\sqrt{11}}$$

Whakangāwaritia te tauraro o \frac{16\sqrt{39}}{7\sqrt{11}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{11}.

$$\frac{16\sqrt{39}\sqrt{11}}{7\left(\sqrt{11}\right)^{2}}$$

Ko te pūrua o \sqrt{11} ko 11.

$$\frac{16\sqrt{39}\sqrt{11}}{7\times 11}$$

Hei whakarea \sqrt{39} me \sqrt{11}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{16\sqrt{429}}{7\times 11}$$

Whakareatia te 7 ki te 11, ka 77.

$$\frac{16\sqrt{429}}{77}$$