Whakaoti i te 3/4sqrt{24}div9sqrt{2}*(2/3sqrt{32})

$$\frac { 3 } { 4 } \sqrt { 24 } \div 9 \sqrt { 2 } \times ( \frac { 2 } { 3 } \sqrt { 32 } )$$

Aromātai

$$\frac{8\sqrt{6}}{9}\approx 2.177324216$$

Ngā Upane Otinga

Tauwehea te 32=2\times 16. Tuhia anō te pūtake rua o te hua \sqrt{2\times 16} hei hua o ngā pūtake rua \sqrt{2}\sqrt{16}.

$$\frac{\frac{3}{4}\sqrt{24}}{9}\sqrt{2}\times \frac{2}{3}\sqrt{2}\sqrt{16}$$

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

$$\frac{\frac{3}{4}\sqrt{24}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Tauwehea te 24=2^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 6} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{6}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\frac{3}{4}\times 2\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Tuhia te \frac{3}{4}\times 2 hei hautanga kotahi.

$$\frac{\frac{3\times 2}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{\frac{6}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{3}{2}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Whakawehea te \frac{3}{2}\sqrt{6} ki te 9, kia riro ko \frac{1}{6}\sqrt{6}.

$$\frac{1}{6}\sqrt{6}\times 2\times \frac{2}{3}\sqrt{16}$$

Whakareatia te \frac{1}{6} ki te 2, ka \frac{2}{6}.

$$\frac{2}{6}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

Whakahekea te hautanga \frac{2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{3}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

Me whakarea te \frac{1}{3} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1\times 2}{3\times 3}\sqrt{6}\sqrt{16}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 2}{3\times 3}.

$$\frac{2}{9}\sqrt{6}\sqrt{16}$$

Tātaitia te pūtakerua o 16 kia tae ki 4.

$$\frac{2}{9}\sqrt{6}\times 4$$

Tuhia te \frac{2}{9}\times 4 hei hautanga kotahi.

$$\frac{2\times 4}{9}\sqrt{6}$$

Whakareatia te 2 ki te 4, ka 8.

$$\frac{8}{9}\sqrt{6}$$