Whakaoti i te frac{sqrt{2}}{sqrt{3}+sqrt{8}}

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

Aromātai

$$\frac{4-\sqrt{6}}{5}\approx 0.310102051$$

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}.

$$\frac{\sqrt{2}}{\sqrt{3}+2\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{3}+2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}-2\sqrt{2}.

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

Whakaarohia te \left(\sqrt{3}+2\sqrt{2}\right)\left(\sqrt{3}-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}.

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

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

$$\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-4\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-4\times 2}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-8}$$

Tangohia te 8 i te 3, ka -5.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{2} ki te \sqrt{3}-2\sqrt{2}.

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

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te -2 ki te 2, ka -4.

$$\frac{\sqrt{6}-4}{-5}$$

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

$$\frac{-\sqrt{6}+4}{5}$$