Issolvi 3*sqrt{18}+1/5sqrt{50}-4*sqrt{1/2}

$$3 \times \sqrt { 18 } + \frac { 1 } { 5 } \sqrt { 50 } - 4 \times \sqrt { \frac { 1 } { 2 } }$$

Evalwa

$$8\sqrt{2}\approx 11.313708499$$

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}.

$$3\times 3\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

Immultiplika 3 u 3 biex tikseb 9.

$$9\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

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}.

$$9\sqrt{2}+\frac{1}{5}\times 5\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Annulla 5 u 5.

$$9\sqrt{2}+\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Ikkombina 9\sqrt{2} u \sqrt{2} biex tikseb 10\sqrt{2}.

$$10\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{2}}.

$$10\sqrt{2}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

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

$$10\sqrt{2}-4\times \frac{1}{\sqrt{2}}$$

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

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{2}$$

Ikkanċella l-akbar fattur komuni 2 f'4 u 2.

$$10\sqrt{2}-2\sqrt{2}$$

Ikkombina 10\sqrt{2} u -2\sqrt{2} biex tikseb 8\sqrt{2}.

$$8\sqrt{2}$$