Whakaoti i te frac{sqrt{5}}{4-sqrt{3}}

$$\frac{ \sqrt{ 5 } }{ 4- \sqrt{ 3 } }$$

Aromātai

$$\frac{\sqrt{5}\left(\sqrt{3}+4\right)}{13}\approx 0.985942712$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{4-\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 4+\sqrt{3}.

$$\frac{\sqrt{5}\left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}$$

Whakaarohia te \left(4-\sqrt{3}\right)\left(4+\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}.

$$\frac{\sqrt{5}\left(4+\sqrt{3}\right)}{4^{2}-\left(\sqrt{3}\right)^{2}}$$

Pūrua 4. Pūrua \sqrt{3}.

$$\frac{\sqrt{5}\left(4+\sqrt{3}\right)}{16-3}$$

Tangohia te 3 i te 16, ka 13.

$$\frac{\sqrt{5}\left(4+\sqrt{3}\right)}{13}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{5} ki te 4+\sqrt{3}.

$$\frac{4\sqrt{5}+\sqrt{5}\sqrt{3}}{13}$$

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{4\sqrt{5}+\sqrt{15}}{13}$$