Whakaoti i te frac{3+sqrt{5}}{sqrt{7}-sqrt{3}}

$$\frac { 3 + \sqrt { 5 } } { \sqrt { 7 } - \sqrt { 3 } }$$

Aromātai

$$\frac{\sqrt{15}+\sqrt{35}+3\sqrt{3}+3\sqrt{7}}{4}\approx 5.730617371$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{3+\sqrt{5}}{\sqrt{7}-\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}+\sqrt{3}.

$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}$$

Whakaarohia te \left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\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}.

$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

Pūrua \sqrt{7}. Pūrua \sqrt{3}.

$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{7-3}$$

Tangohia te 3 i te 7, ka 4.

$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{4}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3+\sqrt{5} ki ia tau o \sqrt{7}+\sqrt{3}.

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{5}\sqrt{7}+\sqrt{5}\sqrt{3}}{4}$$

Hei whakarea \sqrt{5} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{5}\sqrt{3}}{4}$$

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

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{15}}{4}$$