Whakaoti i te 14/5sqrt{3-sqrt{5}}

$$\frac{ 14 }{ 5 \sqrt{ 3 } - \sqrt{ 5 } }$$

Aromātai

$$\frac{\sqrt{5}\left(\sqrt{15}+1\right)}{5}\approx 2.179264403$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{14}{5\sqrt{3}-\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te 5\sqrt{3}+\sqrt{5}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right)}$$

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

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Whakarohaina te \left(5\sqrt{3}\right)^{2}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\times 3-\left(\sqrt{5}\right)^{2}}$$

Whakareatia te 25 ki te 3, ka 75.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-5}$$

Tangohia te 5 i te 75, ka 70.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{70}$$

Whakawehea te 14\left(5\sqrt{3}+\sqrt{5}\right) ki te 70, kia riro ko \frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right).

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

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

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

Me whakakore te 5 me te 5.

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