Whakaoti i te sqrt{(35/26)^2+(161/78)^2}

$$\sqrt { ( \frac { 35 } { 26 } ) ^ { 2 } + ( \frac { 161 } { 78 } ) ^ { 2 } }$$

Aromātai

$$\frac{7\sqrt{754}}{78}\approx 2.464274654$$

Ngā Upane Otinga

Tātaihia te \frac{35}{26} mā te pū o 2, kia riro ko \frac{1225}{676}.

$$\sqrt{\frac{1225}{676}+\left(\frac{161}{78}\right)^{2}}$$

Tātaihia te \frac{161}{78} mā te pū o 2, kia riro ko \frac{25921}{6084}.

$$\sqrt{\frac{1225}{676}+\frac{25921}{6084}}$$

Ko te maha noa iti rawa atu o 676 me 6084 ko 6084. Me tahuri \frac{1225}{676} me \frac{25921}{6084} ki te hautau me te tautūnga 6084.

$$\sqrt{\frac{11025}{6084}+\frac{25921}{6084}}$$

Tā te mea he rite te tauraro o \frac{11025}{6084} me \frac{25921}{6084}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{11025+25921}{6084}}$$

Tāpirihia te 11025 ki te 25921, ka 36946.

$$\sqrt{\frac{36946}{6084}}$$

Whakahekea te hautanga \frac{36946}{6084} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 26.

$$\sqrt{\frac{1421}{234}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1421}{234}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1421}}{\sqrt{234}}.

$$\frac{\sqrt{1421}}{\sqrt{234}}$$

Tauwehea te 1421=7^{2}\times 29. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 29} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{29}. Tuhia te pūtakerua o te 7^{2}.

$$\frac{7\sqrt{29}}{\sqrt{234}}$$

Tauwehea te 234=3^{2}\times 26. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 26} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{26}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{7\sqrt{29}}{3\sqrt{26}}$$

Whakangāwaritia te tauraro o \frac{7\sqrt{29}}{3\sqrt{26}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{26}.

$$\frac{7\sqrt{29}\sqrt{26}}{3\left(\sqrt{26}\right)^{2}}$$

Ko te pūrua o \sqrt{26} ko 26.

$$\frac{7\sqrt{29}\sqrt{26}}{3\times 26}$$

Hei whakarea \sqrt{29} me \sqrt{26}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{7\sqrt{754}}{3\times 26}$$

Whakareatia te 3 ki te 26, ka 78.

$$\frac{7\sqrt{754}}{78}$$