Whakaoti i te sqrt{(8/13)^2-(2/13)^2}

$$\sqrt { ( \frac { 8 } { 13 } ) ^ { 2 } - ( \frac { 2 } { 13 } ) ^ { 2 } }$$

Aromātai

$$\frac{2\sqrt{15}}{13}\approx 0.595843592$$

Ngā Upane Otinga

Tātaihia te \frac{8}{13} mā te pū o 2, kia riro ko \frac{64}{169}.

$$\sqrt{\frac{64}{169}-\left(\frac{2}{13}\right)^{2}}$$

Tātaihia te \frac{2}{13} mā te pū o 2, kia riro ko \frac{4}{169}.

$$\sqrt{\frac{64}{169}-\frac{4}{169}}$$

Tā te mea he rite te tauraro o \frac{64}{169} me \frac{4}{169}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{64-4}{169}}$$

Tangohia te 4 i te 64, ka 60.

$$\sqrt{\frac{60}{169}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{60}{169}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{60}}{\sqrt{169}}.

$$\frac{\sqrt{60}}{\sqrt{169}}$$

Tauwehea te 60=2^{2}\times 15. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 15} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{15}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{15}}{\sqrt{169}}$$

Tātaitia te pūtakerua o 169 kia tae ki 13.

$$\frac{2\sqrt{15}}{13}$$