Issolvi 4sqrt{8}-10sqrt{50}+10sqrt{200}

$$4 \sqrt{ 8 } -10 \sqrt{ 50 } +10 \sqrt{ 200 }$$

Evalwa

$$58\sqrt{2}\approx 82.024386618$$

Passi tas-Soluzzjonijiet

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$4\times 2\sqrt{2}-10\sqrt{50}+10\sqrt{200}$$

Immultiplika 4 u 2 biex tikseb 8.

$$8\sqrt{2}-10\sqrt{50}+10\sqrt{200}$$

Iffattura 50=5^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 5^{2}.

$$8\sqrt{2}-10\times 5\sqrt{2}+10\sqrt{200}$$

Immultiplika -10 u 5 biex tikseb -50.

$$8\sqrt{2}-50\sqrt{2}+10\sqrt{200}$$

Ikkombina 8\sqrt{2} u -50\sqrt{2} biex tikseb -42\sqrt{2}.

$$-42\sqrt{2}+10\sqrt{200}$$

Iffattura 200=10^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{10^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{10^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 10^{2}.

$$-42\sqrt{2}+10\times 10\sqrt{2}$$

Immultiplika 10 u 10 biex tikseb 100.

$$-42\sqrt{2}+100\sqrt{2}$$

Ikkombina -42\sqrt{2} u 100\sqrt{2} biex tikseb 58\sqrt{2}.

$$58\sqrt{2}$$