Whakaoti i te 2/3sqrt{7/15}*3/4sqrt{10/21}

$$\frac { 2 } { 3 } \sqrt { \frac { 7 } { 15 } } \times \frac { 3 } { 4 } \sqrt { \frac { 10 } { 21 } }$$

Aromātai

$$\frac{\sqrt{2}}{6}\approx 0.23570226$$

Ngā Upane Otinga

Hei whakarea \sqrt{\frac{7}{15}} me \sqrt{\frac{10}{21}}, whakareatia ngā tau i raro i te pūtake rua.

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

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{9}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{9}}.

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

Tātaitia te pūtakerua o 9 kia tae ki 3.

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

Me whakarea te \frac{2}{3} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

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

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

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

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

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

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

Whakareatia te 2 ki te 3, ka 6.

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