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

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

Aromātai

$$\frac{2}{3}\approx 0.666666667$$

Ngā Upane Otinga

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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.

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

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

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

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

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

Whakareatia te 4 ki te 1, ka 4.

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

Tāpirihia te \frac{1}{4} ki te 4, ka \frac{17}{4}.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-2^{2}\right)$$

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

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-4\right)$$

Tangohia te 4 i te \frac{17}{4}, ka \frac{1}{4}.

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

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

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

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

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 4 ki te 3, ka 12.

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

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

$$\frac{1}{2}\times \frac{12}{9}$$

Whakahekea te hautanga \frac{12}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Whakareatia te \frac{1}{2} ki te \frac{4}{3}, ka \frac{2}{3}.

$$\frac{2}{3}$$

Tauwehe

$$\frac{2}{3} = 0.6666666666666666$$