Whakaoti i te frac{1+sqrt{25}}{sqrt{3}+sqrt{5}}=

$$\frac { 1 + \sqrt { 25 } } { \sqrt { 3 } + \sqrt { 5 } } =$$

Aromātai

$$3\left(\sqrt{5}-\sqrt{3}\right)\approx 1.51205151$$

Ngā Upane Otinga

Tātaitia te pūtakerua o 25 kia tae ki 5.

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

Tāpirihia te 1 ki te 5, ka 6.

$$\frac{6}{\sqrt{3}+\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{6}{\sqrt{3}+\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}-\sqrt{5}.

$$\frac{6\left(\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{5}\right)}$$

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}.

$$\frac{6\left(\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Pūrua \sqrt{3}. Pūrua \sqrt{5}.

$$\frac{6\left(\sqrt{3}-\sqrt{5}\right)}{3-5}$$

Tangohia te 5 i te 3, ka -2.

$$\frac{6\left(\sqrt{3}-\sqrt{5}\right)}{-2}$$

Whakawehea te 6\left(\sqrt{3}-\sqrt{5}\right) ki te -2, kia riro ko -3\left(\sqrt{3}-\sqrt{5}\right).

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

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

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