Whakaoti i te [(sqrt{3})^2-2*(1/2)^2-3/4*(sqrt{2})^2-4(2/sqrt{3})^2]

$$[ ( \sqrt { 3 } ) ^ { 2 } - 2 \times ( \frac { 1 } { 2 } ) ^ { 2 } - \frac { 3 } { 4 } \times ( \sqrt { 2 } ) ^ { 2 } - 4 ( \frac { 2 } { \sqrt { 3 } } ) ^ { 2 } ]$$

Aromātai

$$-\frac{13}{3}\approx -4.333333333$$

Ngā Upane Otinga

Ko te pūrua o \sqrt{3} ko 3.

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

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

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

Whakareatia te 2 ki te \frac{1}{4}, ka \frac{1}{2}.

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

Tangohia te \frac{1}{2} i te 3, ka \frac{5}{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te \frac{3}{4} ki te 2, ka \frac{3}{2}.

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

Tangohia te \frac{3}{2} i te \frac{5}{2}, ka 1.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Kia whakarewa i te \frac{2\sqrt{3}}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Tuhia te 4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}} hei hautanga kotahi.

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

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{3} ko 3.

$$1-\frac{4\times 4\times 3}{3^{2}}$$

Whakareatia te 4 ki te 3, ka 12.

$$1-\frac{4\times 12}{3^{2}}$$

Whakareatia te 4 ki te 12, ka 48.

$$1-\frac{48}{3^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$1-\frac{48}{9}$$

Whakahekea te hautanga \frac{48}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$1-\frac{16}{3}$$

Tangohia te \frac{16}{3} i te 1, ka -\frac{13}{3}.

$$-\frac{13}{3}$$

Tauwehe

$$-\frac{13}{3} = -4\frac{1}{3} = -4.333333333333333$$