Whakaoti i te -5sqrt{8/27}*sqrt{11/4}*(-3sqrt{54})

$$- 5 \sqrt { \frac { 8 } { 27 } } \times \sqrt { 1 \frac { 1 } { 4 } } \times ( - 3 \sqrt { 54 } )$$

Aromātai

$$30\sqrt{5}\approx 67.082039325$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{27}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{27}}.

$$-5\times \frac{\sqrt{8}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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}.

$$-5\times \frac{2\sqrt{2}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$-5\times \frac{2\sqrt{2}}{3\sqrt{3}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Ko te pūrua o \sqrt{3} ko 3.

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{6}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Whakareatia te 3 ki te 3, ka 9.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Tāpirihia te 4 ki te 1, ka 5.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{5}{4}}\left(-3\right)\sqrt{54}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{4}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{4}}.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{\sqrt{4}}\left(-3\right)\sqrt{54}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\left(-3\right)\sqrt{54}$$

Whakareatia te -5 ki te -3, ka 15.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{54}$$

Tauwehea te 54=3^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 6} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{6}. Tuhia te pūtakerua o te 3^{2}.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\times 3\sqrt{6}$$

Whakareatia te 15 ki te 3, ka 45.

$$45\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 9 i roto i te 45 me te 9.

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

Tuhia te 5\times 2\sqrt{6}\times \frac{\sqrt{5}}{2} hei hautanga kotahi.

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

Me whakakore te 2 me te 2.

$$5\sqrt{6}\sqrt{5}\sqrt{6}$$

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

$$5\times 6\sqrt{5}$$

Whakareatia te 5 ki te 6, ka 30.

$$30\sqrt{5}$$