Whakaoti i te 5/sqrt{6-sqrt{8}}

$$\frac{ 5 }{ \sqrt{ 6 } - \sqrt{ 8 } }$$

Aromātai

$$-\frac{5\sqrt{6}}{2}-5\sqrt{2}\approx -13.194792169$$

Ngā Upane Otinga

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

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

Whakangāwaritia te tauraro o \frac{5}{\sqrt{6}-2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}+2\sqrt{2}.

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

Whakaarohia te \left(\sqrt{6}-2\sqrt{2}\right)\left(\sqrt{6}+2\sqrt{2}\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}.

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

Ko te pūrua o \sqrt{6} ko 6.

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

Whakarohaina te \left(-2\sqrt{2}\right)^{2}.

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

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$\frac{5\left(\sqrt{6}+2\sqrt{2}\right)}{6-4\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{5\left(\sqrt{6}+2\sqrt{2}\right)}{6-4\times 2}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{5\left(\sqrt{6}+2\sqrt{2}\right)}{6-8}$$

Tangohia te 8 i te 6, ka -2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te \sqrt{6}+2\sqrt{2}.

$$\frac{5\sqrt{6}+10\sqrt{2}}{-2}$$