Whakaoti i te sqrt{12}-sqrt{3}+sqrt{1/3}-sqrt[3]{27}

$$\sqrt{ 12 } - \sqrt{ 3 } + \sqrt{ \frac{ 1 }{ 3 } } - \sqrt[3]{ 27 }$$

Aromātai

$$\frac{4\sqrt{3}}{3}-3\approx -0.690598923$$

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}.

$$2\sqrt{3}-\sqrt{3}+\sqrt{\frac{1}{3}}-\sqrt[3]{27}$$

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

$$\sqrt{3}+\sqrt{\frac{1}{3}}-\sqrt[3]{27}$$

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

$$\sqrt{3}+\frac{\sqrt{1}}{\sqrt{3}}-\sqrt[3]{27}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\sqrt{3}+\frac{1}{\sqrt{3}}-\sqrt[3]{27}$$

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

$$\sqrt{3}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt[3]{27}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\sqrt{3}+\frac{\sqrt{3}}{3}-\sqrt[3]{27}$$

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

$$\frac{4}{3}\sqrt{3}-\sqrt[3]{27}$$

Tātaitia te \sqrt[3]{27} kia tae ki 3.

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