Whakaoti i te 2/5-sqrt{3}

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

Aromātai

$$\frac{\sqrt{3}+5}{11}\approx 0.612004619$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{2}{5-\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 5+\sqrt{3}.

$$\frac{2\left(5+\sqrt{3}\right)}{\left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right)}$$

Whakaarohia te \left(5-\sqrt{3}\right)\left(5+\sqrt{3}\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}.

$$\frac{2\left(5+\sqrt{3}\right)}{5^{2}-\left(\sqrt{3}\right)^{2}}$$

Pūrua 5. Pūrua \sqrt{3}.

$$\frac{2\left(5+\sqrt{3}\right)}{25-3}$$

Tangohia te 3 i te 25, ka 22.

$$\frac{2\left(5+\sqrt{3}\right)}{22}$$

Whakawehea te 2\left(5+\sqrt{3}\right) ki te 22, kia riro ko \frac{1}{11}\left(5+\sqrt{3}\right).

$$\frac{1}{11}\left(5+\sqrt{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{11} ki te 5+\sqrt{3}.

$$\frac{1}{11}\times 5+\frac{1}{11}\sqrt{3}$$

Whakareatia te \frac{1}{11} ki te 5, ka \frac{5}{11}.

$$\frac{5}{11}+\frac{1}{11}\sqrt{3}$$