Whakaoti i te 6sqrt{5}div(-2sqrt{5/2})

$$6 \sqrt { 5 } \div ( - 2 \sqrt { \frac { 5 } { 2 } } )$$

Aromātai

$$-3\sqrt{2}\approx -4.242640687$$

Ngā Upane Otinga

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{3\sqrt{5}}{-\sqrt{\frac{5}{2}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{3\sqrt{5}}{-\frac{\sqrt{5}}{\sqrt{2}}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{3\sqrt{5}}{-\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{3\sqrt{5}}{-\frac{\sqrt{5}\sqrt{2}}{2}}$$

Hei whakarea \sqrt{5} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{3\sqrt{5}}{-\frac{\sqrt{10}}{2}}$$

Me whakakore tahi te -1 i te taurunga me te tauraro.

$$\frac{-3\sqrt{5}}{\frac{\sqrt{10}}{2}}$$

Whakawehe -3\sqrt{5} ki te \frac{\sqrt{10}}{2} mā te whakarea -3\sqrt{5} ki te tau huripoki o \frac{\sqrt{10}}{2}.

$$\frac{-3\sqrt{5}\times 2}{\sqrt{10}}$$

Whakareatia te -3 ki te 2, ka -6.

$$\frac{-6\sqrt{5}}{\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{-6\sqrt{5}}{\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{-6\sqrt{5}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{-6\sqrt{5}\sqrt{10}}{10}$$

Tauwehea te 10=5\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5\times 2} hei hua o ngā pūtake rua \sqrt{5}\sqrt{2}.

$$\frac{-6\sqrt{5}\sqrt{5}\sqrt{2}}{10}$$

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

$$\frac{-6\times 5\sqrt{2}}{10}$$

Whakawehea te -6\times 5\sqrt{2} ki te 10, kia riro ko -\frac{3}{5}\times 5\sqrt{2}.

$$-\frac{3}{5}\times 5\sqrt{2}$$

Me whakakore te 5 me te 5.

$$-3\sqrt{2}$$