Whakaoti i te {left(sqrt{2}-sqrt{3}right)}^2-2sqrt{1/3}*3sqrt{12}

$${ \left( \sqrt{ 2 } - \sqrt{ 3 } \right) }^{ 2 } -2 \sqrt{ \frac{ 1 }{ 3 } } \times 3 \sqrt{ 12 }$$

Aromātai

$$-2\sqrt{6}-7\approx -11.898979486$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{2}-\sqrt{3}\right)^{2}.

$$\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

Ko te pūrua o \sqrt{2} ko 2.

$$2-2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

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

$$2-2\sqrt{6}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

Ko te pūrua o \sqrt{3} ko 3.

$$2-2\sqrt{6}+3-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

Tāpirihia te 2 ki te 3, ka 5.

$$5-2\sqrt{6}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

Whakareatia te 2 ki te 3, ka 6.

$$5-2\sqrt{6}-6\sqrt{\frac{1}{3}}\sqrt{12}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$5-2\sqrt{6}-6\times \frac{\sqrt{1}}{\sqrt{3}}\sqrt{12}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$5-2\sqrt{6}-6\times \frac{1}{\sqrt{3}}\sqrt{12}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{12}$$

Ko te pūrua o \sqrt{3} ko 3.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{3}\sqrt{12}$$

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}.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{3}\times 2\sqrt{3}$$

Whakareatia te 6 ki te 2, ka 12.

$$5-2\sqrt{6}-12\times \frac{\sqrt{3}}{3}\sqrt{3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 12 me te 3.

$$5-2\sqrt{6}-4\sqrt{3}\sqrt{3}$$

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

$$5-2\sqrt{6}-4\times 3$$

Whakareatia te 4 ki te 3, ka 12.

$$5-2\sqrt{6}-12$$

Tangohia te 12 i te 5, ka -7.

$$-7-2\sqrt{6}$$