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

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

Evalwa

$$37\sqrt{29}+57\sqrt{10}+134\sqrt{5}+100\approx 779.134033479$$

Passi tas-Soluzzjonijiet

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

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

Ikkalkula 60 bil-power ta' 2 u tikseb 3600.

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

Żid 400 u 3600 biex tikseb 4000.

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

Iffattura 4000=20^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{20^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{20^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 20^{2}.

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

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

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

Ikkalkula 40 bil-power ta' 2 u tikseb 1600.

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

Żid 400 u 1600 biex tikseb 2000.

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

Iffattura 2000=20^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{20^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{20^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 20^{2}.

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

Ikkalkula 40 bil-power ta' 2 u tikseb 1600.

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

Ikkalkula 80 bil-power ta' 2 u tikseb 6400.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{1600+6400}+1.85\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Żid 1600 u 6400 biex tikseb 8000.

$$20\sqrt{10}+100+20\sqrt{5}+\sqrt{8000}+1.85\sqrt{40^{2}+80^{2}}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Iffattura 8000=40^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{40^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{40^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 40^{2}.

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

Ikkombina 20\sqrt{5} u 40\sqrt{5} biex tikseb 60\sqrt{5}.

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

Ikkalkula 40 bil-power ta' 2 u tikseb 1600.

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

Ikkalkula 80 bil-power ta' 2 u tikseb 6400.

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

Żid 1600 u 6400 biex tikseb 8000.

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

Iffattura 8000=40^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{40^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{40^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 40^{2}.

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

Immultiplika 1.85 u 40 biex tikseb 74.

$$20\sqrt{10}+100+60\sqrt{5}+74\sqrt{5}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ikkombina 60\sqrt{5} u 74\sqrt{5} biex tikseb 134\sqrt{5}.

$$20\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{20^{2}+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

$$20\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{400+60^{2}}+1.85\sqrt{40^{2}+100^{2}}$$

Ikkalkula 60 bil-power ta' 2 u tikseb 3600.

$$20\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{400+3600}+1.85\sqrt{40^{2}+100^{2}}$$

Żid 400 u 3600 biex tikseb 4000.

$$20\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{4000}+1.85\sqrt{40^{2}+100^{2}}$$

Iffattura 4000=20^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{20^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{20^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 20^{2}.

$$20\sqrt{10}+100+134\sqrt{5}+1.85\times 20\sqrt{10}+1.85\sqrt{40^{2}+100^{2}}$$

Immultiplika 1.85 u 20 biex tikseb 37.

$$20\sqrt{10}+100+134\sqrt{5}+37\sqrt{10}+1.85\sqrt{40^{2}+100^{2}}$$

Ikkombina 20\sqrt{10} u 37\sqrt{10} biex tikseb 57\sqrt{10}.

$$57\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{40^{2}+100^{2}}$$

Ikkalkula 40 bil-power ta' 2 u tikseb 1600.

$$57\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{1600+100^{2}}$$

Ikkalkula 100 bil-power ta' 2 u tikseb 10000.

$$57\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{1600+10000}$$

Żid 1600 u 10000 biex tikseb 11600.

$$57\sqrt{10}+100+134\sqrt{5}+1.85\sqrt{11600}$$

Iffattura 11600=20^{2}\times 29. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{20^{2}\times 29} bħala l-prodott tal-għeruq kwadrati \sqrt{20^{2}}\sqrt{29}. Ħu l-għerq kwadrat ta' 20^{2}.

$$57\sqrt{10}+100+134\sqrt{5}+1.85\times 20\sqrt{29}$$

Immultiplika 1.85 u 20 biex tikseb 37.

$$57\sqrt{10}+100+134\sqrt{5}+37\sqrt{29}$$

Fattur

$$37 \sqrt{29} + 57 \sqrt{10} + 134 \sqrt{5} + 100 = 779.134033479$$