Whakaoti i te (sqrt{6}-sqrt{2})^2-frac{sqrt{6}-sqrt{2}}{sqrt{6}+sqrt{2}}

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

Aromātai

$$6-3\sqrt{3}\approx 0.803847577$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{6}-\sqrt{2}\right)^{2}.

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

Ko te pūrua o \sqrt{6} ko 6.

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

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}.

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

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

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

Whakareatia te -2 ki te 2, ka -4.

$$6-4\sqrt{3}+\left(\sqrt{2}\right)^{2}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$6-4\sqrt{3}+2-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

Tāpirihia te 6 ki te 2, ka 8.

$$8-4\sqrt{3}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}-\sqrt{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}$$

Whakaarohia te \left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Pūrua \sqrt{6}. Pūrua \sqrt{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{6-2}$$

Tangohia te 2 i te 6, ka 4.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{4}$$

Whakareatia te \sqrt{6}-\sqrt{2} ki te \sqrt{6}-\sqrt{2}, ka \left(\sqrt{6}-\sqrt{2}\right)^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)^{2}}{4}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{6}-\sqrt{2}\right)^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}\right)^{2}-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

Ko te pūrua o \sqrt{6} ko 6.

$$8-4\sqrt{3}-\frac{6-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

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}.

$$8-4\sqrt{3}-\frac{6-2\sqrt{2}\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

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

$$8-4\sqrt{3}-\frac{6-2\times 2\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

Whakareatia te -2 ki te 2, ka -4.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

Ko te pūrua o \sqrt{2} ko 2.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+2}{4}$$

Tāpirihia te 6 ki te 2, ka 8.

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

Whakawehea ia wā o 8-4\sqrt{3} ki te 4, kia riro ko 2-\sqrt{3}.

$$8-4\sqrt{3}-\left(2-\sqrt{3}\right)$$

Hei kimi i te tauaro o 2-\sqrt{3}, kimihia te tauaro o ia taurangi.

$$8-4\sqrt{3}-2+\sqrt{3}$$

Tangohia te 2 i te 8, ka 6.

$$6-4\sqrt{3}+\sqrt{3}$$

Pahekotia te -4\sqrt{3} me \sqrt{3}, ka -3\sqrt{3}.

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

Tauwehe

$$3 {(2 - \sqrt{3})} = 0.803847577$$