Whakaoti i te -4sqrt{21/5}divsqrt{41/11}=

$$- 4 \sqrt { 2 \frac { 1 } { 5 } } \div \sqrt { 4 \frac { 1 } { 11 } } =$$

Aromātai

$$-\frac{44}{15}\approx -2.933333333$$

Ngā Upane Otinga

Whakareatia te 2 ki te 5, ka 10.

$$\frac{-4\sqrt{\frac{10+1}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Tāpirihia te 10 ki te 1, ka 11.

$$\frac{-4\sqrt{\frac{11}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{11}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{11}}{\sqrt{5}}.

$$\frac{-4\times \frac{\sqrt{11}}{\sqrt{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{11}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Hei whakarea \sqrt{11} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{-4\times \frac{\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Tuhia te -4\times \frac{\sqrt{55}}{5} hei hautanga kotahi.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Whakareatia te 4 ki te 11, ka 44.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{44+1}{11}}}$$

Tāpirihia te 44 ki te 1, ka 45.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{45}{11}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{45}{11}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{45}}{\sqrt{11}}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{\sqrt{45}}{\sqrt{11}}}$$

Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}}{\sqrt{11}}}$$

Whakangāwaritia te tauraro o \frac{3\sqrt{5}}{\sqrt{11}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{11}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}}$$

Ko te pūrua o \sqrt{11} ko 11.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{11}}$$

Hei whakarea \sqrt{5} me \sqrt{11}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{55}}{11}}$$

Whakawehe \frac{-4\sqrt{55}}{5} ki te \frac{3\sqrt{55}}{11} mā te whakarea \frac{-4\sqrt{55}}{5} ki te tau huripoki o \frac{3\sqrt{55}}{11}.

$$\frac{-4\sqrt{55}\times 11}{5\times 3\sqrt{55}}$$

Me whakakore tahi te \sqrt{55} i te taurunga me te tauraro.

$$\frac{-4\times 11}{3\times 5}$$

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

$$\frac{4\times 11}{-3\times 5}$$

Whakareatia te 4 ki te 11, ka 44.

$$\frac{44}{-3\times 5}$$

Whakareatia te -3 ki te 5, ka -15.

$$\frac{44}{-15}$$

Ka taea te hautanga \frac{44}{-15} te tuhi anō ko -\frac{44}{15} mā te tango i te tohu tōraro.

$$-\frac{44}{15}$$

Tauwehe

$$-\frac{44}{15} = -2\frac{14}{15} = -2.933333333333333$$