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

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

Aromātai

$$\frac{\sqrt{2}+4}{7}\approx 0.77345908$$

Ngā Upane Otinga

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

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

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

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

Pūrua 3. Pūrua \sqrt{2}.

$$\frac{\left(2+\sqrt{2}\right)\left(3-\sqrt{2}\right)}{9-2}$$

Tangohia te 2 i te 9, ka 7.

$$\frac{\left(2+\sqrt{2}\right)\left(3-\sqrt{2}\right)}{7}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2+\sqrt{2} ki ia tau o 3-\sqrt{2}.

$$\frac{6-2\sqrt{2}+3\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

Pahekotia te -2\sqrt{2} me 3\sqrt{2}, ka \sqrt{2}.

$$\frac{6+\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{6+\sqrt{2}-2}{7}$$

Tangohia te 2 i te 6, ka 4.

$$\frac{4+\sqrt{2}}{7}$$

Tauwehe

$$\frac{\sqrt{2} + 4}{7} = 0.7734590803390136$$