Whakaoti i te frac{sqrt{3}}{4}*(2-frac{2sqrt{3}}{3})^2*6

$$\frac { \sqrt { 3 } } { 4 } \times ( 2 - \frac { 2 \sqrt { 3 } } { 3 } ) ^ { 2 } \times 6$$

Aromātai

$$8\sqrt{3}-12\approx 1.856406461$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2 ki te \frac{3}{3}.

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

Tā te mea he rite te tauraro o \frac{2\times 3}{3} me \frac{2\sqrt{3}}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 2\times 3-2\sqrt{3}.

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

Kia whakarewa i te \frac{6-2\sqrt{3}}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Tuhia te 6\times \frac{\sqrt{3}}{4} hei hautanga kotahi.

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

Me whakarea te \frac{6\sqrt{3}}{4} ki te \frac{\left(6-2\sqrt{3}\right)^{2}}{3^{2}} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Me whakakore tahi te 2\times 3 i te taurunga me te tauraro.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-2\sqrt{3}+6\right)^{2}.

$$\frac{\sqrt{3}\left(4\left(\sqrt{3}\right)^{2}-24\sqrt{3}+36\right)}{2\times 3}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\sqrt{3}\left(4\times 3-24\sqrt{3}+36\right)}{2\times 3}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{\sqrt{3}\left(12-24\sqrt{3}+36\right)}{2\times 3}$$

Tāpirihia te 12 ki te 36, ka 48.

$$\frac{\sqrt{3}\left(48-24\sqrt{3}\right)}{2\times 3}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{\sqrt{3}\left(48-24\sqrt{3}\right)}{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{3} ki te 48-24\sqrt{3}.

$$\frac{48\sqrt{3}-24\left(\sqrt{3}\right)^{2}}{6}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{48\sqrt{3}-24\times 3}{6}$$

Whakareatia te -24 ki te 3, ka -72.

$$\frac{48\sqrt{3}-72}{6}$$