Whakaoti i te frac{sqrt{2}-sqrt{5}}{sqrt{2}+sqrt{5}}=

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

Aromātai

$$\frac{2\sqrt{10}-7}{3}\approx -0.225148227$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{2}-\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}.

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

Pūrua \sqrt{2}. Pūrua \sqrt{5}.

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

Tangohia te 5 i te 2, ka -3.

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

Whakareatia te \sqrt{2}-\sqrt{5} ki te \sqrt{2}-\sqrt{5}, ka \left(\sqrt{2}-\sqrt{5}\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{2}-\sqrt{5}\right)^{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

$$\frac{2-2\sqrt{10}+\left(\sqrt{5}\right)^{2}}{-3}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{2-2\sqrt{10}+5}{-3}$$

Tāpirihia te 2 ki te 5, ka 7.

$$\frac{7-2\sqrt{10}}{-3}$$

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

$$\frac{-7+2\sqrt{10}}{3}$$