Whakaoti i te frac{-2sqrt{21}sqrt{72}}{sqrt{60}}

$$\frac{ -2 \sqrt{ 21 } \sqrt{ 72 } }{ \sqrt{ 60 } }$$

Aromātai

$$-\frac{6\sqrt{70}}{5}\approx -10.039920318$$

Ngā Upane Otinga

Tauwehea te 72=6^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 2} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{2}. Tuhia te pūtakerua o te 6^{2}.

$$\frac{-2\sqrt{21}\times 6\sqrt{2}}{\sqrt{60}}$$

Whakareatia te -2 ki te 6, ka -12.

$$\frac{-12\sqrt{21}\sqrt{2}}{\sqrt{60}}$$

Hei whakarea \sqrt{21} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{-12\sqrt{42}}{\sqrt{60}}$$

Tauwehea te 60=2^{2}\times 15. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 15} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{15}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{-12\sqrt{42}}{2\sqrt{15}}$$

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

$$\frac{-6\sqrt{42}}{\sqrt{15}}$$

Whakangāwaritia te tauraro o \frac{-6\sqrt{42}}{\sqrt{15}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{15}.

$$\frac{-6\sqrt{42}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

Ko te pūrua o \sqrt{15} ko 15.

$$\frac{-6\sqrt{42}\sqrt{15}}{15}$$

Hei whakarea \sqrt{42} me \sqrt{15}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{-6\sqrt{630}}{15}$$

Tauwehea te 630=3^{2}\times 70. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 70} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{70}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{-6\times 3\sqrt{70}}{15}$$

Whakareatia te -6 ki te 3, ka -18.

$$\frac{-18\sqrt{70}}{15}$$

Whakawehea te -18\sqrt{70} ki te 15, kia riro ko -\frac{6}{5}\sqrt{70}.

$$-\frac{6}{5}\sqrt{70}$$