Whakaoti i te frac{(4-sqrt{5})(4+sqrt{5})}{2sqrt{11}}

$$\frac { ( 4 - \sqrt { 5 } ) ( 4 + \sqrt { 5 } ) } { 2 \sqrt { 11 } }$$

Aromātai

$$\frac{\sqrt{11}}{2}\approx 1.658312395$$

Ngā Upane Otinga

Whakaarohia te \left(4-\sqrt{5}\right)\left(4+\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}.

$$\frac{4^{2}-\left(\sqrt{5}\right)^{2}}{2\sqrt{11}}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{16-\left(\sqrt{5}\right)^{2}}{2\sqrt{11}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{16-5}{2\sqrt{11}}$$

Tangohia te 5 i te 16, ka 11.

$$\frac{11}{2\sqrt{11}}$$

Whakangāwaritia te tauraro o \frac{11}{2\sqrt{11}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{11}.

$$\frac{11\sqrt{11}}{2\left(\sqrt{11}\right)^{2}}$$

Ko te pūrua o \sqrt{11} ko 11.

$$\frac{11\sqrt{11}}{2\times 11}$$

Me whakakore tahi te 11 i te taurunga me te tauraro.

$$\frac{\sqrt{11}}{2}$$