Whakaoti i te -{[(1/sqrt{2})-(-1/sqrt{5})]+(-sqrt{4})^3+2(sqrt{16}-1/2)}div(3/4)

$$- \{ [ ( \frac { 1 } { \sqrt { 2 } } ) - ( - \frac { 1 } { \sqrt { 5 } } ) ] + ( - \sqrt { 4 } ) ^ { 3 } + 2 ( \sqrt { 16 } - \frac { 1 } { 2 } ) \} \div ( \frac { 3 } { 4 } )$$

Aromātai

$$-\frac{2\sqrt{2}}{3}-\frac{4\sqrt{5}}{15}+\frac{4}{3}\approx -0.205760502$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{1}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{-\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-2\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Tātaihia te -2 mā te pū o 3, kia riro ko -8.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Tātaitia te pūtakerua o 16 kia tae ki 4.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(4-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Tangohia te \frac{1}{2} i te 4, ka \frac{7}{2}.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\times \frac{7}{2}\right)}{\frac{3}{4}}$$

Whakareatia te 2 ki te \frac{7}{2}, ka 7.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+7\right)}{\frac{3}{4}}$$

Tāpirihia te -8 ki te 7, ka -1.

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

Hei kimi i te tauaro o \frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-1, kimihia te tauaro o ia taurangi.

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

Whakawehe -\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 ki te \frac{3}{4} mā te whakarea -\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 ki te tau huripoki o \frac{3}{4}.

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

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

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 5 ko 10. Whakareatia \frac{\sqrt{2}}{2} ki te \frac{5}{5}. Whakareatia \frac{\sqrt{5}}{5} ki te \frac{2}{2}.

$$\frac{\left(-\left(\frac{5\sqrt{2}}{10}+\frac{2\sqrt{5}}{10}\right)+1\right)\times 4}{3}$$

Tā te mea he rite te tauraro o \frac{5\sqrt{2}}{10} me \frac{2\sqrt{5}}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+1\right)\times 4}{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{10}{10}.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+\frac{10}{10}\right)\times 4}{3}$$

Tā te mea he rite te tauraro o -\frac{5\sqrt{2}+2\sqrt{5}}{10} me \frac{10}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{-\left(5\sqrt{2}+2\sqrt{5}\right)+10}{10}\times 4}{3}$$

Mahia ngā whakarea i roto o -\left(5\sqrt{2}+2\sqrt{5}\right)+10.

$$\frac{\frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4}{3}$$

Tuhia te \frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4 hei hautanga kotahi.

$$\frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3}$$

Tuhia te \frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3} hei hautanga kotahi.

$$\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10\times 3}$$

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

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{3\times 5}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{15}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -5\sqrt{2}-2\sqrt{5}+10.

$$\frac{-10\sqrt{2}-4\sqrt{5}+20}{15}$$