Whakaoti i te frac{sqrt{2}}{sqrt{3}-sqrt{5}}

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

Aromātai

$$\frac{-\sqrt{6}-\sqrt{10}}{2}\approx -2.805883701$$

Ngā Upane Otinga

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

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

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

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

Pūrua \sqrt{3}. Pūrua \sqrt{5}.

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

Tangohia te 5 i te 3, ka -2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{2} ki te \sqrt{3}+\sqrt{5}.

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

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{6}+\sqrt{2}\sqrt{5}}{-2}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{6}+\sqrt{10}}{-2}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-\sqrt{6}-\sqrt{10}}{2}$$