Whakaoti i te frac{2sqrt{2}}{5-2sqrt{6}}

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

Aromātai

$$8\sqrt{3}+10\sqrt{2}\approx 27.998542084$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\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}.

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

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}}$$

Whakarohaina te \left(-2\sqrt{6}\right)^{2}.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\times 6}$$

Whakareatia te 4 ki te 6, ka 24.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-24}$$

Tangohia te 24 i te 25, ka 1.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{1}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

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

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

$$10\sqrt{2}+4\sqrt{2}\sqrt{6}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

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

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$10\sqrt{2}+4\times 2\sqrt{3}$$

Whakareatia te 4 ki te 2, ka 8.

$$10\sqrt{2}+8\sqrt{3}$$