Issolvi 5sqrt{50}-2sqrt{18}+9sqrt{32}

$$5 \sqrt { 50 } - 2 \sqrt { 18 } + 9 \sqrt { 32 }$$

Evalwa

$$55\sqrt{2}\approx 77.781745931$$

Passi tas-Soluzzjonijiet

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}.

$$5\times 5\sqrt{2}-2\sqrt{18}+9\sqrt{32}$$

Immultiplika 5 u 5 biex tikseb 25.

$$25\sqrt{2}-2\sqrt{18}+9\sqrt{32}$$

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$25\sqrt{2}-2\times 3\sqrt{2}+9\sqrt{32}$$

Immultiplika -2 u 3 biex tikseb -6.

$$25\sqrt{2}-6\sqrt{2}+9\sqrt{32}$$

Ikkombina 25\sqrt{2} u -6\sqrt{2} biex tikseb 19\sqrt{2}.

$$19\sqrt{2}+9\sqrt{32}$$

Iffattura 32=4^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 4^{2}.

$$19\sqrt{2}+9\times 4\sqrt{2}$$

Immultiplika 9 u 4 biex tikseb 36.

$$19\sqrt{2}+36\sqrt{2}$$

Ikkombina 19\sqrt{2} u 36\sqrt{2} biex tikseb 55\sqrt{2}.

$$55\sqrt{2}$$