Whakaoti i te frac{2sqrt{3}}{7+sqrt{6}}

$$\frac { 2 \sqrt { 3 } } { 7 + \sqrt { 6 } }$$

Aromātai

$$\frac{14\sqrt{3}-6\sqrt{2}}{43}\approx 0.366591394$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{2\sqrt{3}}{7+\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te 7-\sqrt{6}.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{\left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right)}$$

Whakaarohia te \left(7+\sqrt{6}\right)\left(7-\sqrt{6}\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}.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}$$

Pūrua 7. Pūrua \sqrt{6}.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{49-6}$$

Tangohia te 6 i te 49, ka 43.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{43}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2\sqrt{3} ki te 7-\sqrt{6}.

$$\frac{14\sqrt{3}-2\sqrt{3}\sqrt{6}}{43}$$

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}.

$$\frac{14\sqrt{3}-2\sqrt{3}\sqrt{3}\sqrt{2}}{43}$$

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

$$\frac{14\sqrt{3}-2\times 3\sqrt{2}}{43}$$

Whakareatia te -2 ki te 3, ka -6.

$$\frac{14\sqrt{3}-6\sqrt{2}}{43}$$