Whakaoti i te 2/sqrt{8+sqrt{7}}=

$$\frac { 2 } { \sqrt { 8 } + \sqrt { 7 } } =$$

Aromātai

$$2^{\frac{5}{2}}-2\sqrt{7}\approx 0.365351627$$

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}.

$$\frac{2}{2\sqrt{2}+\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{2}{2\sqrt{2}+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{2}-\sqrt{7}.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{\left(2\sqrt{2}+\sqrt{7}\right)\left(2\sqrt{2}-\sqrt{7}\right)}$$

Whakaarohia te \left(2\sqrt{2}+\sqrt{7}\right)\left(2\sqrt{2}-\sqrt{7}\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}.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{\left(2\sqrt{2}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$

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

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{2^{2}\left(\sqrt{2}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$

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

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{4\left(\sqrt{2}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{4\times 2-\left(\sqrt{7}\right)^{2}}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{8-\left(\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{8-7}$$

Tangohia te 7 i te 8, ka 1.

$$\frac{2\left(2\sqrt{2}-\sqrt{7}\right)}{1}$$

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

$$2\left(2\sqrt{2}-\sqrt{7}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 2\sqrt{2}-\sqrt{7}.

$$4\sqrt{2}-2\sqrt{7}$$