Whakaoti i te 36/5:(-5/6)^-1+sqrt{27/16}-1/8-frac{13}{4}=

$$\frac { 36 } { 5 } : ( - \frac { 5 } { 6 } ) ^ { - 1 } + \sqrt { \frac { 27 } { 16 } } - \frac { 1 } { 8 } - \frac { 13 } { 4 } =$$

Aromātai

$$\frac{3\sqrt{3}}{4}-\frac{75}{8}\approx -8.075961894$$

Ngā Hipanga Rongoā Poto

Tātaihia te -\frac{5}{6} mā te pū o -1, kia riro ko -\frac{6}{5}.

$$\frac{\frac{36}{5}}{-\frac{6}{5}}+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

Whakawehe \frac{36}{5} ki te -\frac{6}{5} mā te whakarea \frac{36}{5} ki te tau huripoki o -\frac{6}{5}.

$$\frac{36}{5}\left(-\frac{5}{6}\right)+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

Whakareatia te \frac{36}{5} ki te -\frac{5}{6}, ka -6.

$$-6+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{27}{16}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{27}}{\sqrt{16}}.

$$-6+\frac{\sqrt{27}}{\sqrt{16}}-\frac{1}{8}-\frac{13}{4}$$

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}.

$$-6+\frac{3\sqrt{3}}{\sqrt{16}}-\frac{1}{8}-\frac{13}{4}$$

Tātaitia te pūtakerua o 16 kia tae ki 4.

$$-6+\frac{3\sqrt{3}}{4}-\frac{1}{8}-\frac{13}{4}$$

Tangohia te \frac{1}{8} i te -6, ka -\frac{49}{8}.

$$-\frac{49}{8}+\frac{3\sqrt{3}}{4}-\frac{13}{4}$$

Tangohia te \frac{13}{4} i te -\frac{49}{8}, ka -\frac{75}{8}.

$$-\frac{75}{8}+\frac{3\sqrt{3}}{4}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 8 me 4 ko 8. Whakareatia \frac{3\sqrt{3}}{4} ki te \frac{2}{2}.

$$-\frac{75}{8}+\frac{2\times 3\sqrt{3}}{8}$$

Tā te mea he rite te tauraro o -\frac{75}{8} me \frac{2\times 3\sqrt{3}}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-75+2\times 3\sqrt{3}}{8}$$

Mahia ngā whakarea i roto o -75+2\times 3\sqrt{3}.

$$\frac{-75+6\sqrt{3}}{8}$$

Tauwehe

$$\frac{3 {(2 \sqrt{3} - 25)}}{8} = -8.075961894323342$$