Réitigh 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}

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

Luacháil

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

Céimeanna Réitigh

Ríomh cumhacht 20 de 2 agus faigh 400.

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

Ríomh cumhacht 60 de 2 agus faigh 3600.

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

Suimigh 400 agus 3600 chun 4000 a fháil.

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

Fachtóirigh 4000=20^{2}\times 10. Athscríobh fréamh cearnach an toraidh \sqrt{20^{2}\times 10} mar thoradh na bhfréamhacha cearnacha \sqrt{20^{2}}\sqrt{10}. Tóg fréamh chearnach 20^{2}.

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

Ríomh cumhacht 20 de 2 agus faigh 400.

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

Ríomh cumhacht 40 de 2 agus faigh 1600.

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

Suimigh 400 agus 1600 chun 2000 a fháil.

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

Fachtóirigh 2000=20^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{20^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{20^{2}}\sqrt{5}. Tóg fréamh chearnach 20^{2}.

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

Ríomh cumhacht 40 de 2 agus faigh 1600.

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

Ríomh cumhacht 80 de 2 agus faigh 6400.

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

Suimigh 1600 agus 6400 chun 8000 a fháil.

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

Fachtóirigh 8000=40^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{40^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{40^{2}}\sqrt{5}. Tóg fréamh chearnach 40^{2}.

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

Comhcheangail 20\sqrt{5} agus 40\sqrt{5} chun 60\sqrt{5} a fháil.

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

Ríomh cumhacht 100 de 2 agus faigh 10000.

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

Ríomh cumhacht 20 de 2 agus faigh 400.

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

Suimigh 10000 agus 400 chun 10400 a fháil.

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

Fachtóirigh 10400=20^{2}\times 26. Athscríobh fréamh cearnach an toraidh \sqrt{20^{2}\times 26} mar thoradh na bhfréamhacha cearnacha \sqrt{20^{2}}\sqrt{26}. Tóg fréamh chearnach 20^{2}.

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

Ríomh cumhacht 20 de 2 agus faigh 400.

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

Ríomh cumhacht 60 de 2 agus faigh 3600.

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

Suimigh 400 agus 3600 chun 4000 a fháil.

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

Fachtóirigh 4000=20^{2}\times 10. Athscríobh fréamh cearnach an toraidh \sqrt{20^{2}\times 10} mar thoradh na bhfréamhacha cearnacha \sqrt{20^{2}}\sqrt{10}. Tóg fréamh chearnach 20^{2}.

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

Comhcheangail 20\sqrt{10} agus 20\sqrt{10} chun 40\sqrt{10} a fháil.

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

Ríomh cumhacht 40 de 2 agus faigh 1600.

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

Ríomh cumhacht 100 de 2 agus faigh 10000.

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

Suimigh 1600 agus 10000 chun 11600 a fháil.

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

Fachtóirigh 11600=20^{2}\times 29. Athscríobh fréamh cearnach an toraidh \sqrt{20^{2}\times 29} mar thoradh na bhfréamhacha cearnacha \sqrt{20^{2}}\sqrt{29}. Tóg fréamh chearnach 20^{2}.

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

Ríomh cumhacht 40 de 2 agus faigh 1600.

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

Ríomh cumhacht 80 de 2 agus faigh 6400.

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

Suimigh 1600 agus 6400 chun 8000 a fháil.

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

Fachtóirigh 8000=40^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{40^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{40^{2}}\sqrt{5}. Tóg fréamh chearnach 40^{2}.

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

Comhcheangail 60\sqrt{5} agus 40\sqrt{5} chun 100\sqrt{5} a fháil.

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

Fachtóirigh

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