Whakaoti i te 5/6(sqrt{3+2)}

$$\frac { 5 } { 6 ( \sqrt { 3 } + 2 ) }$$

Aromātai

$$-\frac{5\sqrt{3}}{6}+\frac{5}{3}\approx 0.223290994$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te \sqrt{3}+2.

$$\frac{5}{6\sqrt{3}+12}$$

Whakangāwaritia te tauraro o \frac{5}{6\sqrt{3}+12} mā te whakarea i te taurunga me te tauraro ki te 6\sqrt{3}-12.

$$\frac{5\left(6\sqrt{3}-12\right)}{\left(6\sqrt{3}+12\right)\left(6\sqrt{3}-12\right)}$$

Whakaarohia te \left(6\sqrt{3}+12\right)\left(6\sqrt{3}-12\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}.

$$\frac{5\left(6\sqrt{3}-12\right)}{\left(6\sqrt{3}\right)^{2}-12^{2}}$$

Whakarohaina te \left(6\sqrt{3}\right)^{2}.

$$\frac{5\left(6\sqrt{3}-12\right)}{6^{2}\left(\sqrt{3}\right)^{2}-12^{2}}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$\frac{5\left(6\sqrt{3}-12\right)}{36\left(\sqrt{3}\right)^{2}-12^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5\left(6\sqrt{3}-12\right)}{36\times 3-12^{2}}$$

Whakareatia te 36 ki te 3, ka 108.

$$\frac{5\left(6\sqrt{3}-12\right)}{108-12^{2}}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$\frac{5\left(6\sqrt{3}-12\right)}{108-144}$$

Tangohia te 144 i te 108, ka -36.

$$\frac{5\left(6\sqrt{3}-12\right)}{-36}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te 6\sqrt{3}-12.

$$\frac{30\sqrt{3}-60}{-36}$$