Whakaoti i te sqrt{20^2+60^2}+sqrt{20^2+40^2}+sqrt{{40}^{2}+{80}^{2}}+sqrt{{100}^{2}+{20}^{2}}+sqrt{{20}^{2}+{60}^{2}}+sqrt{{40}^2+{100}^2}+sqrt{{40}^2+{80}^2}

$$\sqrt{ { 20 }^{ 2 } + { 60 }^{ 2 } } + \sqrt{ { 20 }^{ 2 } + { 40 }^{ 2 } } + \sqrt{ { 40 }^{ 2 } + { 80 }^{ 2 } } + \sqrt{ { 100 }^{ 2 } + { 20 }^{ 2 } } + \sqrt{ { 20 }^{ 2 } + { 60 }^{ 2 } } + \sqrt{ { 40 }^{ 2 } + { 100 }^{ 2 } } + \sqrt{ { 40 }^{ 2 } + { 80 }^{ 2 } }$$

Aromātai

$$20\left(\sqrt{26}+\sqrt{29}+2\sqrt{10}+5\sqrt{5}\right)\approx 559.781590571$$

Ngā Upane Otinga

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$\sqrt{400+60^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 60 mā te pū o 2, kia riro ko 3600.

$$\sqrt{400+3600}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 400 ki te 3600, ka 4000.

$$\sqrt{4000}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 4000=20^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{20^{2}\times 10} hei hua o ngā pūtake rua \sqrt{20^{2}}\sqrt{10}. Tuhia te pūtakerua o te 20^{2}.

$$20\sqrt{10}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$20\sqrt{10}+\sqrt{400+40^{2}}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 40 mā te pū o 2, kia riro ko 1600.

$$20\sqrt{10}+\sqrt{400+1600}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 400 ki te 1600, ka 2000.

$$20\sqrt{10}+\sqrt{2000}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 2000=20^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{20^{2}\times 5} hei hua o ngā pūtake rua \sqrt{20^{2}}\sqrt{5}. Tuhia te pūtakerua o te 20^{2}.

$$20\sqrt{10}+20\sqrt{5}+\sqrt{40^{2}+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 40 mā te pū o 2, kia riro ko 1600.

$$20\sqrt{10}+20\sqrt{5}+\sqrt{1600+80^{2}}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 80 mā te pū o 2, kia riro ko 6400.

$$20\sqrt{10}+20\sqrt{5}+\sqrt{1600+6400}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 1600 ki te 6400, ka 8000.

$$20\sqrt{10}+20\sqrt{5}+\sqrt{8000}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 8000=40^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{40^{2}\times 5} hei hua o ngā pūtake rua \sqrt{40^{2}}\sqrt{5}. Tuhia te pūtakerua o te 40^{2}.

$$20\sqrt{10}+20\sqrt{5}+40\sqrt{5}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Pahekotia te 20\sqrt{5} me 40\sqrt{5}, ka 60\sqrt{5}.

$$20\sqrt{10}+60\sqrt{5}+\sqrt{100^{2}+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$20\sqrt{10}+60\sqrt{5}+\sqrt{10000+20^{2}}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$20\sqrt{10}+60\sqrt{5}+\sqrt{10000+400}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 10000 ki te 400, ka 10400.

$$20\sqrt{10}+60\sqrt{5}+\sqrt{10400}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 10400=20^{2}\times 26. Tuhia anō te pūtake rua o te hua \sqrt{20^{2}\times 26} hei hua o ngā pūtake rua \sqrt{20^{2}}\sqrt{26}. Tuhia te pūtakerua o te 20^{2}.

$$20\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{20^{2}+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$20\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{400+60^{2}}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 60 mā te pū o 2, kia riro ko 3600.

$$20\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{400+3600}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 400 ki te 3600, ka 4000.

$$20\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{4000}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 4000=20^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{20^{2}\times 10} hei hua o ngā pūtake rua \sqrt{20^{2}}\sqrt{10}. Tuhia te pūtakerua o te 20^{2}.

$$20\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{10}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Pahekotia te 20\sqrt{10} me 20\sqrt{10}, ka 40\sqrt{10}.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{40^{2}+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 40 mā te pū o 2, kia riro ko 1600.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{1600+100^{2}}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{1600+10000}+\sqrt{40^{2}+80^{2}}$$

Tāpirihia te 1600 ki te 10000, ka 11600.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+\sqrt{11600}+\sqrt{40^{2}+80^{2}}$$

Tauwehea te 11600=20^{2}\times 29. Tuhia anō te pūtake rua o te hua \sqrt{20^{2}\times 29} hei hua o ngā pūtake rua \sqrt{20^{2}}\sqrt{29}. Tuhia te pūtakerua o te 20^{2}.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{29}+\sqrt{40^{2}+80^{2}}$$

Tātaihia te 40 mā te pū o 2, kia riro ko 1600.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{29}+\sqrt{1600+80^{2}}$$

Tātaihia te 80 mā te pū o 2, kia riro ko 6400.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{29}+\sqrt{1600+6400}$$

Tāpirihia te 1600 ki te 6400, ka 8000.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{29}+\sqrt{8000}$$

Tauwehea te 8000=40^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{40^{2}\times 5} hei hua o ngā pūtake rua \sqrt{40^{2}}\sqrt{5}. Tuhia te pūtakerua o te 40^{2}.

$$40\sqrt{10}+60\sqrt{5}+20\sqrt{26}+20\sqrt{29}+40\sqrt{5}$$

Pahekotia te 60\sqrt{5} me 40\sqrt{5}, ka 100\sqrt{5}.

$$40\sqrt{10}+100\sqrt{5}+20\sqrt{26}+20\sqrt{29}$$

Tauwehe

$$20 {(\sqrt{26} + \sqrt{29} + 2 \sqrt{10} + 5 \sqrt{5})} = 559.781590571$$