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

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

Aromātai

$$-\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{4}\approx 0.270090757$$

Ngā Upane Otinga

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

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

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

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

Pūrua \sqrt{5}. Pūrua 3.

$$\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{5-9}$$

Tangohia te 9 i te 5, ka -4.

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

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

$$\frac{\sqrt{2}\sqrt{5}-3\sqrt{2}}{-4}$$

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

$$\frac{\sqrt{10}-3\sqrt{2}}{-4}$$

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

$$\frac{-\sqrt{10}+3\sqrt{2}}{4}$$