Whakaoti i te 5/2sqrt{7-2sqrt{5}}

$$\frac { 5 } { 2 \sqrt { 7 } - 2 \sqrt { 5 } }$$

Aromātai

$$\frac{5\left(\sqrt{5}+\sqrt{7}\right)}{4}\approx 6.102274111$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{5}{2\sqrt{7}-2\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{7}+2\sqrt{5}.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{\left(2\sqrt{7}-2\sqrt{5}\right)\left(2\sqrt{7}+2\sqrt{5}\right)}$$

Whakaarohia te \left(2\sqrt{7}-2\sqrt{5}\right)\left(2\sqrt{7}+2\sqrt{5}\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}.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{\left(2\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

Whakarohaina te \left(2\sqrt{7}\right)^{2}.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{2^{2}\left(\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\left(\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\times 7-\left(-2\sqrt{5}\right)^{2}}$$

Whakareatia te 4 ki te 7, ka 28.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\sqrt{5}\right)^{2}}$$

Whakarohaina te \left(-2\sqrt{5}\right)^{2}.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\times 5}$$

Whakareatia te 4 ki te 5, ka 20.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-20}$$

Tangohia te 20 i te 28, ka 8.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{8}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te 2\sqrt{7}+2\sqrt{5}.

$$\frac{10\sqrt{7}+10\sqrt{5}}{8}$$