Whakaoti i te 3/3-sqrt{3}

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

Aromātai

$$\frac{\sqrt{3}+3}{2}\approx 2.366025404$$

Ngā Upane Otinga

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

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

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

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

Pūrua 3. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 9, ka 6.

$$\frac{3\left(3+\sqrt{3}\right)}{6}$$

Whakawehea te 3\left(3+\sqrt{3}\right) ki te 6, kia riro ko \frac{1}{2}\left(3+\sqrt{3}\right).

$$\frac{1}{2}\left(3+\sqrt{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 3+\sqrt{3}.

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

Whakareatia te \frac{1}{2} ki te 3, ka \frac{3}{2}.

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