Whakaoti i te frac{sqrt{72}}{sqrt{6}}quadtext{(2)}sqrt{18}divsqrt{8}

$$\frac { \sqrt { 72 } } { \sqrt { 6 } } \quad \text { (2) } \sqrt { 18 } \div \sqrt { 8 }$$

Aromātai

$$6\sqrt{3}\approx 10.392304845$$

Ngā Upane Otinga

Tuhia anō te whakawehe o ngā pūtake rua \frac{\sqrt{72}}{\sqrt{6}} hei pūtake rua o te whakawehenga \sqrt{\frac{72}{6}} ka mahi i te whakawehenga.

$$\frac{\sqrt{12}\times 2\sqrt{18}}{\sqrt{8}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{3}\times 2\sqrt{18}}{\sqrt{8}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{4\sqrt{3}\sqrt{18}}{\sqrt{8}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{4\sqrt{3}\times 3\sqrt{2}}{\sqrt{8}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{12\sqrt{3}\sqrt{2}}{\sqrt{8}}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{12\sqrt{6}}{\sqrt{8}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{12\sqrt{6}}{2\sqrt{2}}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{6\sqrt{6}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{6\sqrt{6}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{6\sqrt{6}\sqrt{2}}{2}$$

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

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

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

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

Me whakakore te 2 me te 2.

$$6\sqrt{3}$$