Whakaoti i te (2sqrt{2}-1)^2-(1+sqrt{3})*(sqrt{2}-sqrt{6})

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } - ( 1 + \sqrt { 3 } ) \times ( \sqrt { 2 } - \sqrt { 6 } )$$

Aromātai

$$9-2\sqrt{2}\approx 6.171572875$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2\sqrt{2}-1\right)^{2}.

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$4\times 2-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Whakareatia te 4 ki te 2, ka 8.

$$8-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Tāpirihia te 8 ki te 1, ka 9.

$$9-4\sqrt{2}-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{3}\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{6}-\sqrt{3}\sqrt{6}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

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}.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{3}\sqrt{2}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-3\sqrt{2}\right)$$

Pahekotia te \sqrt{2} me -3\sqrt{2}, ka -2\sqrt{2}.

$$9-4\sqrt{2}-\left(-2\sqrt{2}\right)$$

Ko te tauaro o -2\sqrt{2} ko 2\sqrt{2}.

$$9-4\sqrt{2}+2\sqrt{2}$$

Pahekotia te -4\sqrt{2} me 2\sqrt{2}, ka -2\sqrt{2}.

$$9-2\sqrt{2}$$