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

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

Aromātai

$$\frac{5\sqrt{3}}{16}-\frac{9}{4}\approx -1.708734123$$

Ngā Hipanga Rongoā Poto

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

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

Tātaihia te \frac{3}{2} mā te pū o 2, kia riro ko \frac{9}{4}.

$$\left(-\frac{\sqrt{3}}{4}\right)\times \frac{9}{4}\left(\sqrt{3}\right)^{2}-\frac{\sqrt{3}}{2}\times \frac{3}{2}\sqrt{3}+2\sqrt{3}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\left(-\frac{\sqrt{3}}{4}\right)\times \frac{9}{4}\times 3-\frac{\sqrt{3}}{2}\times \frac{3}{2}\sqrt{3}+2\sqrt{3}$$

Whakareatia te \frac{9}{4} ki te 3, ka \frac{27}{4}.

$$\left(-\frac{\sqrt{3}}{4}\right)\times \frac{27}{4}-\frac{\sqrt{3}}{2}\times \frac{3}{2}\sqrt{3}+2\sqrt{3}$$

Me whakarea te -\frac{\sqrt{3}}{4} ki te \frac{27}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{\sqrt{3}}{2}\times \frac{3}{2}\sqrt{3}+2\sqrt{3}$$

Me whakarea te \frac{\sqrt{3}}{2} ki te \frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{\sqrt{3}\times 3}{2\times 2}\sqrt{3}+2\sqrt{3}$$

Tuhia te \frac{\sqrt{3}\times 3}{2\times 2}\sqrt{3} hei hautanga kotahi.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{\sqrt{3}\times 3\sqrt{3}}{2\times 2}+2\sqrt{3}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{3\times 3}{2\times 2}+2\sqrt{3}$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{9}{2\times 2}+2\sqrt{3}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{9}{4}+2\sqrt{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4\times 4 me 4 ko 4\times 4. Whakareatia \frac{9}{4} ki te \frac{4}{4}.

$$\frac{-\sqrt{3}\times 27}{4\times 4}-\frac{9\times 4}{4\times 4}+2\sqrt{3}$$

Tā te mea he rite te tauraro o \frac{-\sqrt{3}\times 27}{4\times 4} me \frac{9\times 4}{4\times 4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-\sqrt{3}\times 27-9\times 4}{4\times 4}+2\sqrt{3}$$

Mahia ngā whakarea i roto o -\sqrt{3}\times 27-9\times 4.

$$\frac{-27\sqrt{3}-36}{4\times 4}+2\sqrt{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2\sqrt{3} ki te \frac{4\times 4}{4\times 4}.

$$\frac{-27\sqrt{3}-36}{4\times 4}+\frac{2\sqrt{3}\times 4\times 4}{4\times 4}$$

Tā te mea he rite te tauraro o \frac{-27\sqrt{3}-36}{4\times 4} me \frac{2\sqrt{3}\times 4\times 4}{4\times 4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-27\sqrt{3}-36+2\sqrt{3}\times 4\times 4}{4\times 4}$$

Mahia ngā whakarea i roto o -27\sqrt{3}-36+2\sqrt{3}\times 4\times 4.

$$\frac{-27\sqrt{3}-36+32\sqrt{3}}{4\times 4}$$

Mahia ngā tātaitai i roto o -27\sqrt{3}-36+32\sqrt{3}.

$$\frac{5\sqrt{3}-36}{4\times 4}$$

Whakarohaina te 4\times 4.

$$\frac{5\sqrt{3}-36}{16}$$

Tauwehe

$$\frac{5 \sqrt{3} - 36}{16} = -1.708734122634726$$