Issolvi frac{2sqrt{54}+8sqrt{6}}{6sqrt{12}-5sqrt{3}}

$$\frac { 2 \sqrt { 54 } + 8 \sqrt { 6 } } { 6 \sqrt { 12 } - 5 \sqrt { 3 } }$$

Evalwa

$$2\sqrt{2}\approx 2.828427125$$

Passi tas-Soluzzjonijiet

Iffattura 54=3^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{2\times 3\sqrt{6}+8\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6\sqrt{6}+8\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Ikkombina 6\sqrt{6} u 8\sqrt{6} biex tikseb 14\sqrt{6}.

$$\frac{14\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{14\sqrt{6}}{6\times 2\sqrt{3}-5\sqrt{3}}$$

Immultiplika 6 u 2 biex tikseb 12.

$$\frac{14\sqrt{6}}{12\sqrt{3}-5\sqrt{3}}$$

Ikkombina 12\sqrt{3} u -5\sqrt{3} biex tikseb 7\sqrt{3}.

$$\frac{14\sqrt{6}}{7\sqrt{3}}$$

Annulla 7 fin-numeratur u d-denominatur.

$$\frac{2\sqrt{6}}{\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{6}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{2\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{2\sqrt{6}\sqrt{3}}{3}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

$$\frac{2\sqrt{3}\sqrt{2}\sqrt{3}}{3}$$

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$\frac{2\times 3\sqrt{2}}{3}$$

Annulla 3 u 3.

$$2\sqrt{2}$$