Whakaoti i te 3sqrt{22/3}div2sqrt{2/5}*(-1/8sqrt{15})

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

Aromātai

$$-\frac{3}{4}=-0.75$$

Ngā Upane Otinga

Whakareatia te 2 ki te 3, ka 6.

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

Tāpirihia te 6 ki te 2, ka 8.

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

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

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

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}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

Me whakakore te 3 me te 3.

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

Me whakakore te 2 me te 2.

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

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

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

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

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

Ko te pūrua o \sqrt{5} ko 5.

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

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

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

Tuhia te \sqrt{6}\times \frac{\sqrt{10}}{5} hei hautanga kotahi.

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

Me whakarea te \frac{\sqrt{6}\sqrt{10}}{5} ki te -\frac{1}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Tuhia te \frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15} hei hautanga kotahi.

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

Hei whakarea \sqrt{6} me \sqrt{10}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{-\sqrt{60}\sqrt{15}}{5\times 8}$$

Tauwehea te 60=15\times 4. Tuhia anō te pūtake rua o te hua \sqrt{15\times 4} hei hua o ngā pūtake rua \sqrt{15}\sqrt{4}.

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

Whakareatia te \sqrt{15} ki te \sqrt{15}, ka 15.

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

Whakareatia te 5 ki te 8, ka 40.

$$\frac{-15\sqrt{4}}{40}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{-15\times 2}{40}$$

Whakareatia te -15 ki te 2, ka -30.

$$\frac{-30}{40}$$

Whakahekea te hautanga \frac{-30}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$-\frac{3}{4}$$

Tauwehe

$$-\frac{3}{4} = -0.75$$