Whakaoti i te -6^2*2:(2+2*sqrt{27})=

$$- 6 ^ { 2 } \cdot 2 : ( 2 + 2 \cdot \sqrt { 27 } ) =$$

Aromātai

$$\frac{18-54\sqrt{3}}{13}\approx -5.810057201$$

Ngā Upane Otinga

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$\frac{-36\times 2}{2+2\sqrt{27}}$$

Whakareatia te -36 ki te 2, ka -72.

$$\frac{-72}{2+2\sqrt{27}}$$

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}.

$$\frac{-72}{2+2\times 3\sqrt{3}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{-72}{2+6\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{-72}{2+6\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 2-6\sqrt{3}.

$$\frac{-72\left(2-6\sqrt{3}\right)}{\left(2+6\sqrt{3}\right)\left(2-6\sqrt{3}\right)}$$

Whakaarohia te \left(2+6\sqrt{3}\right)\left(2-6\sqrt{3}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-72\left(2-6\sqrt{3}\right)}{2^{2}-\left(6\sqrt{3}\right)^{2}}$$

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

$$\frac{-72\left(2-6\sqrt{3}\right)}{4-\left(6\sqrt{3}\right)^{2}}$$

Whakarohaina te \left(6\sqrt{3}\right)^{2}.

$$\frac{-72\left(2-6\sqrt{3}\right)}{4-6^{2}\left(\sqrt{3}\right)^{2}}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$\frac{-72\left(2-6\sqrt{3}\right)}{4-36\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{-72\left(2-6\sqrt{3}\right)}{4-36\times 3}$$

Whakareatia te 36 ki te 3, ka 108.

$$\frac{-72\left(2-6\sqrt{3}\right)}{4-108}$$

Tangohia te 108 i te 4, ka -104.

$$\frac{-72\left(2-6\sqrt{3}\right)}{-104}$$

Whakawehea te -72\left(2-6\sqrt{3}\right) ki te -104, kia riro ko \frac{9}{13}\left(2-6\sqrt{3}\right).

$$\frac{9}{13}\left(2-6\sqrt{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{9}{13} ki te 2-6\sqrt{3}.

$$\frac{9}{13}\times 2+\frac{9}{13}\left(-6\right)\sqrt{3}$$

Tuhia te \frac{9}{13}\times 2 hei hautanga kotahi.

$$\frac{9\times 2}{13}+\frac{9}{13}\left(-6\right)\sqrt{3}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{18}{13}+\frac{9}{13}\left(-6\right)\sqrt{3}$$

Tuhia te \frac{9}{13}\left(-6\right) hei hautanga kotahi.

$$\frac{18}{13}+\frac{9\left(-6\right)}{13}\sqrt{3}$$

Whakareatia te 9 ki te -6, ka -54.

$$\frac{18}{13}+\frac{-54}{13}\sqrt{3}$$

Ka taea te hautanga \frac{-54}{13} te tuhi anō ko -\frac{54}{13} mā te tango i te tohu tōraro.

$$\frac{18}{13}-\frac{54}{13}\sqrt{3}$$