Issolvi 2sqrt{18}-4sqrt{1/8}+sqrt{32}+0

$$2 \sqrt{ 18 } -4 \sqrt{ \frac{ 1 }{ 8 } } + \sqrt{ 32 } +0$$

Evalwa

$$9\sqrt{2}\approx 12.727922061$$

Passi tas-Soluzzjonijiet

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}.

$$2\times 3\sqrt{2}-4\sqrt{\frac{1}{8}}+\sqrt{32}+0$$

Immultiplika 2 u 3 biex tikseb 6.

$$6\sqrt{2}-4\sqrt{\frac{1}{8}}+\sqrt{32}+0$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{8}}.

$$6\sqrt{2}-4\times \frac{\sqrt{1}}{\sqrt{8}}+\sqrt{32}+0$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$6\sqrt{2}-4\times \frac{1}{\sqrt{8}}+\sqrt{32}+0$$

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}.

$$6\sqrt{2}-4\times \frac{1}{2\sqrt{2}}+\sqrt{32}+0$$

Irrazzjonalizza d-denominatur tal-\frac{1}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{32}+0$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{2\times 2}+\sqrt{32}+0$$

Immultiplika 2 u 2 biex tikseb 4.

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{4}+\sqrt{32}+0$$

Annulla 4 u 4.

$$6\sqrt{2}-\sqrt{2}+\sqrt{32}+0$$

Ikkombina 6\sqrt{2} u -\sqrt{2} biex tikseb 5\sqrt{2}.

$$5\sqrt{2}+\sqrt{32}+0$$

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}.

$$5\sqrt{2}+4\sqrt{2}+0$$

Ikkombina 5\sqrt{2} u 4\sqrt{2} biex tikseb 9\sqrt{2}.

$$9\sqrt{2}+0$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$9\sqrt{2}$$