Whakaoti i te 3sqrt{2frac{2/3}}{1/2}sqrt{2/5}*(-1/8sqrt{15})

$$\frac{ 3 \sqrt{ 2 \frac{ 2 }{ 3 } } }{ \frac{ 1 }{ 2 } } \sqrt{ \frac{ 2 }{ 5 } } \times (- \frac{ 1 }{ 8 } \sqrt{ 15 } )$$

Aromātai

$$-3$$

Ngā Upane Otinga

Whakareatia te 2 ki te 3, ka 6.

$$\frac{3\sqrt{\frac{6+2}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tāpirihia te 6 ki te 2, ka 8.

$$\frac{3\sqrt{\frac{8}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{3\times \frac{\sqrt{8}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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}.

$$\frac{3\times \frac{2\sqrt{2}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Me whakakore te 3 me te 3.

$$\frac{2\sqrt{6}}{\frac{1}{2}}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Whakawehe 2\sqrt{6} ki te \frac{1}{2} mā te whakarea 2\sqrt{6} ki te tau huripoki o \frac{1}{2}.

$$2\sqrt{6}\times 2\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{6}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{5}}.

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Ko te pūrua o \sqrt{5} ko 5.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tuhia te 4\left(-\frac{1}{8}\right) hei hautanga kotahi.

$$\frac{4\left(-1\right)}{8}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Whakareatia te 4 ki te -1, ka -4.

$$\frac{-4}{8}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Whakahekea te hautanga \frac{-4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{1}{2}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Me whakarea te -\frac{1}{2} ki te \frac{\sqrt{10}}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\sqrt{10}}{2\times 5}\sqrt{6}\sqrt{15}$$

Tuhia te \frac{-\sqrt{10}}{2\times 5}\sqrt{15} hei hautanga kotahi.

$$\frac{-\sqrt{10}\sqrt{15}}{2\times 5}\sqrt{6}$$

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

$$\frac{-\sqrt{150}}{2\times 5}\sqrt{6}$$

Whakareatia te 2 ki te 5, ka 10.

$$\frac{-\sqrt{150}}{10}\sqrt{6}$$

Tauwehea te 150=5^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 6} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{6}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{-5\sqrt{6}}{10}\sqrt{6}$$

Whakawehea te -5\sqrt{6} ki te 10, kia riro ko -\frac{1}{2}\sqrt{6}.

$$-\frac{1}{2}\sqrt{6}\sqrt{6}$$

Whakareatia te \sqrt{6} ki te \sqrt{6}, ka 6.

$$-\frac{1}{2}\times 6$$

Tuhia te -\frac{1}{2}\times 6 hei hautanga kotahi.

$$\frac{-6}{2}$$

Whakawehea te -6 ki te 2, kia riro ko -3.

$$-3$$

Tauwehe

$$-3$$