Whakaoti i te sqrt{1-12/25+60/169/2}

$$\sqrt { \frac { 1 - \frac { 12 } { 25 } + \frac { 60 } { 169 } } { 2 } }$$

Aromātai

$$\frac{\sqrt{7394}}{130}\approx 0.66144901$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{25}{25}.

$$\sqrt{\frac{\frac{25}{25}-\frac{12}{25}+\frac{60}{169}}{2}}$$

Tā te mea he rite te tauraro o \frac{25}{25} me \frac{12}{25}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{\frac{25-12}{25}+\frac{60}{169}}{2}}$$

Tangohia te 12 i te 25, ka 13.

$$\sqrt{\frac{\frac{13}{25}+\frac{60}{169}}{2}}$$

Ko te maha noa iti rawa atu o 25 me 169 ko 4225. Me tahuri \frac{13}{25} me \frac{60}{169} ki te hautau me te tautūnga 4225.

$$\sqrt{\frac{\frac{2197}{4225}+\frac{1500}{4225}}{2}}$$

Tā te mea he rite te tauraro o \frac{2197}{4225} me \frac{1500}{4225}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{\frac{2197+1500}{4225}}{2}}$$

Tāpirihia te 2197 ki te 1500, ka 3697.

$$\sqrt{\frac{\frac{3697}{4225}}{2}}$$

Tuhia te \frac{\frac{3697}{4225}}{2} hei hautanga kotahi.

$$\sqrt{\frac{3697}{4225\times 2}}$$

Whakareatia te 4225 ki te 2, ka 8450.

$$\sqrt{\frac{3697}{8450}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3697}{8450}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3697}}{\sqrt{8450}}.

$$\frac{\sqrt{3697}}{\sqrt{8450}}$$

Tauwehea te 8450=65^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{65^{2}\times 2} hei hua o ngā pūtake rua \sqrt{65^{2}}\sqrt{2}. Tuhia te pūtakerua o te 65^{2}.

$$\frac{\sqrt{3697}}{65\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{3697}}{65\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\sqrt{3697}\sqrt{2}}{65\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{3697}\sqrt{2}}{65\times 2}$$

Hei whakarea \sqrt{3697} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{7394}}{65\times 2}$$

Whakareatia te 65 ki te 2, ka 130.

$$\frac{\sqrt{7394}}{130}$$