Whakaoti i te 1/3sqrt{3+3sqrt{2}}

$$\frac{ 1 }{ 3 \sqrt{ 3 } +3 \sqrt{ 2 } }$$

Aromātai

$$\frac{\sqrt{3}-\sqrt{2}}{3}\approx 0.105945748$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1}{3\sqrt{3}+3\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 3\sqrt{3}-3\sqrt{2}.

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

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

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

Whakarohaina te \left(3\sqrt{3}\right)^{2}.

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

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 9 ki te 3, ka 27.

$$\frac{3\sqrt{3}-3\sqrt{2}}{27-\left(3\sqrt{2}\right)^{2}}$$

Whakarohaina te \left(3\sqrt{2}\right)^{2}.

$$\frac{3\sqrt{3}-3\sqrt{2}}{27-3^{2}\left(\sqrt{2}\right)^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{3\sqrt{3}-3\sqrt{2}}{27-9\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{3\sqrt{3}-3\sqrt{2}}{27-9\times 2}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{3\sqrt{3}-3\sqrt{2}}{27-18}$$

Tangohia te 18 i te 27, ka 9.

$$\frac{3\sqrt{3}-3\sqrt{2}}{9}$$

Tauwehe

$$\frac{\sqrt{3} - \sqrt{2}}{3} = 0.10594574839859401$$