Whakaoti i te frac{left(sqrt{6}-sqrt{12}right)*sqrt{3}}{sqrt{6}}+sqrt{6}

$$\frac{ \left( \sqrt{ 6 } - \sqrt{ 12 } \right) \times \sqrt{ 3 } }{ \sqrt{ 6 } } + \sqrt{ 6 }$$

Aromātai

$$\sqrt{3}\approx 1.732050808$$

Ngā Upane Otinga

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}}+\sqrt{6}$$

Whakangāwaritia te tauraro o \frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}+\sqrt{6}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}\sqrt{6}}{6}+\sqrt{6}$$

Tauwehea te 6=3\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3\times 2} hei hua o ngā pūtake rua \sqrt{3}\sqrt{2}.

$$\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}\sqrt{3}\sqrt{2}}{6}+\sqrt{6}$$

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

$$\frac{\left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2}}{6}+\sqrt{6}$$

Whakawehea te \left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2} ki te 6, kia riro ko \left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}.

$$\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}+\sqrt{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{6}-2\sqrt{3} ki te \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-2\sqrt{3}\times \frac{1}{2}\right)\sqrt{2}+\sqrt{6}$$

Whakareatia -2 ki te \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-\sqrt{3}\right)\sqrt{2}+\sqrt{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{6}\times \frac{1}{2}-\sqrt{3} ki te \sqrt{2}.

$$\sqrt{6}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$\sqrt{2}\sqrt{3}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$2\times \frac{1}{2}\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Me whakakore te 2 me te 2.

$$\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\sqrt{3}-\sqrt{6}+\sqrt{6}$$

Pahekotia te -\sqrt{6} me \sqrt{6}, ka 0.

$$\sqrt{3}$$