Whakaoti i te sqrt{3/4}*(-sqrt{22/3})*sqrt{56}

$$\sqrt { \frac { 3 } { 4 } } \times ( - \sqrt { 2 \frac { 2 } { 3 } } ) \times \sqrt { 56 }$$

Aromātai

$$-4\sqrt{7}\approx -10.583005244$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{4}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{4}}.

$$\frac{\sqrt{3}}{\sqrt{4}}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{6+2}{3}}\right)\sqrt{56}$$

Tāpirihia te 6 ki te 2, ka 8.

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{8}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{\sqrt{8}}{\sqrt{3}}\right)\sqrt{56}$$

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}.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}}{\sqrt{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\sqrt{56}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{3}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\sqrt{56}$$

Tauwehea te 56=2^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 14} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{14}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\times 2\sqrt{14}$$

Me whakarea te \frac{\sqrt{3}}{2} ki te -\frac{2\sqrt{6}}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\sqrt{3}\times 2\sqrt{6}}{2\times 3}\times 2\sqrt{14}$$

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

$$\frac{-\sqrt{3}\sqrt{6}}{3}\times 2\sqrt{14}$$

Tuhia te \frac{-\sqrt{3}\sqrt{6}}{3}\times 2 hei hautanga kotahi.

$$\frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14}$$

Tuhia te \frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14} hei hautanga kotahi.

$$\frac{-\sqrt{3}\sqrt{6}\times 2\sqrt{14}}{3}$$

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

$$\frac{-\sqrt{3}\sqrt{3}\sqrt{2}\times 2\sqrt{14}}{3}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{-3\sqrt{2}\times 2\sqrt{14}}{3}$$

Tauwehea te 14=2\times 7. Tuhia anō te pūtake rua o te hua \sqrt{2\times 7} hei hua o ngā pūtake rua \sqrt{2}\sqrt{7}.

$$\frac{-3\sqrt{2}\times 2\sqrt{2}\sqrt{7}}{3}$$

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

$$\frac{-3\times 2\times 2\sqrt{7}}{3}$$

Whakareatia te -3 ki te 2, ka -6.

$$\frac{-6\times 2\sqrt{7}}{3}$$

Whakareatia te -6 ki te 2, ka -12.

$$\frac{-12\sqrt{7}}{3}$$

Whakawehea te -12\sqrt{7} ki te 3, kia riro ko -4\sqrt{7}.

$$-4\sqrt{7}$$