Whakaoti i te sqrt{8}div(sqrt{2}-1)

$$\sqrt { 8 } \div ( \sqrt { 2 } - 1 )$$

Aromātai

$$2\sqrt{2}+4\approx 6.828427125$$

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}.

$$\frac{2\sqrt{2}}{\sqrt{2}-1}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{2}}{\sqrt{2}-1} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}+1.

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

Whakaarohia te \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\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}.

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

Pūrua \sqrt{2}. Pūrua 1.

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

Tangohia te 1 i te 2, ka 1.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2\sqrt{2} ki te \sqrt{2}+1.

$$2\left(\sqrt{2}\right)^{2}+2\sqrt{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\times 2+2\sqrt{2}$$

Whakareatia te 2 ki te 2, ka 4.

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