Réitigh sqrt{20^2+60^2}+100+sqrt{20^2+40^2}+sqrt{{20}^{2}+{40}^{2}}+sqrt{{40}^{2}+{80}^{2}}+1.85*sqrt{{20}^2+{60}^2}+1.85*sqrt{{40}^2+{100}^2}

$$\sqrt{ { 20 }^{ 2 } + { 60 }^{ 2 } } +100+ \sqrt{ { 20 }^{ 2 } + { 40 }^{ 2 } } + \sqrt{ { 20 }^{ 2 } + { 40 }^{ 2 } } + \sqrt{ { 40 }^{ 2 } + { 80 }^{ 2 } } +1.85 \times \sqrt{ { 20 }^{ 2 } + { 60 }^{ 2 } } +1.85 \times \sqrt{ { 40 }^{ 2 } + { 100 }^{ 2 } }$$

Luacháil

$$37\sqrt{29}+57\sqrt{10}+80\sqrt{5}+100\approx 658.386362694$$

Céimeanna Réitigh

Ríomh cumhacht 20 de 2 agus faigh 400.

$$\sqrt{400+60^{2}}+100+\sqrt{20^{2}+40^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 60 de 2 agus faigh 3600.

$$\sqrt{400+3600}+100+\sqrt{20^{2}+40^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Suimigh 400 agus 3600 chun 4000 a fháil.

$$\sqrt{4000}+100+\sqrt{20^{2}+40^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

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}.

$$20\sqrt{10}+100+\sqrt{20^{2}+40^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 20 de 2 agus faigh 400.

$$20\sqrt{10}+100+\sqrt{400+40^{2}}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 40 de 2 agus faigh 1600.

$$20\sqrt{10}+100+\sqrt{400+1600}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Suimigh 400 agus 1600 chun 2000 a fháil.

$$20\sqrt{10}+100+\sqrt{2000}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

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}.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{20^{2}+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 20 de 2 agus faigh 400.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{400+40^{2}}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 40 de 2 agus faigh 1600.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{400+1600}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Suimigh 400 agus 1600 chun 2000 a fháil.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{2000}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

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}.

$$20\sqrt{10}+100+20\sqrt{5}+20\sqrt{5}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

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

$$20\sqrt{10}+100+40\sqrt{5}+\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 40 de 2 agus faigh 1600.

$$20\sqrt{10}+100+40\sqrt{5}+\sqrt{1600+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 80 de 2 agus faigh 6400.

$$20\sqrt{10}+100+40\sqrt{5}+\sqrt{1600+6400}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Suimigh 1600 agus 6400 chun 8000 a fháil.

$$20\sqrt{10}+100+40\sqrt{5}+\sqrt{8000}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

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}.

$$20\sqrt{10}+100+40\sqrt{5}+40\sqrt{5}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Comhcheangail 40\sqrt{5} agus 40\sqrt{5} chun 80\sqrt{5} a fháil.

$$20\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 20 de 2 agus faigh 400.

$$20\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{400+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 60 de 2 agus faigh 3600.

$$20\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{400+3600}+1.85\sqrt{40^{2}+100^{2}}$$

Suimigh 400 agus 3600 chun 4000 a fháil.

$$20\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{4000}+1.85\sqrt{40^{2}+100^{2}}$$

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}.

$$20\sqrt{10}+100+80\sqrt{5}+1.85\times 20\sqrt{10}+1.85\sqrt{40^{2}+100^{2}}$$

Méadaigh 1.85 agus 20 chun 37 a fháil.

$$20\sqrt{10}+100+80\sqrt{5}+37\sqrt{10}+1.85\sqrt{40^{2}+100^{2}}$$

Comhcheangail 20\sqrt{10} agus 37\sqrt{10} chun 57\sqrt{10} a fháil.

$$57\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{40^{2}+100^{2}}$$

Ríomh cumhacht 40 de 2 agus faigh 1600.

$$57\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{1600+100^{2}}$$

Ríomh cumhacht 100 de 2 agus faigh 10000.

$$57\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{1600+10000}$$

Suimigh 1600 agus 10000 chun 11600 a fháil.

$$57\sqrt{10}+100+80\sqrt{5}+1.85\sqrt{11600}$$

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}.

$$57\sqrt{10}+100+80\sqrt{5}+1.85\times 20\sqrt{29}$$

Méadaigh 1.85 agus 20 chun 37 a fháil.

$$57\sqrt{10}+100+80\sqrt{5}+37\sqrt{29}$$

Fachtóirigh

$$37 \sqrt{29} + 57 \sqrt{10} + 80 \sqrt{5} + 100 = 658.386362694$$