Issolvi 2/sqrt{3}+12/sqrt{27}+2sqrt{7}

$$\frac { 2 } { \sqrt { 3 } } + \frac { 12 } { \sqrt { 27 } } + 2 \sqrt { 7 }$$

Evalwa

$$2\left(\sqrt{3}+\sqrt{7}\right)\approx 8.755604237$$

Passi tas-Soluzzjonijiet

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

$$\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{12}{\sqrt{27}}+2\sqrt{7}$$

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

$$\frac{2\sqrt{3}}{3}+\frac{12}{\sqrt{27}}+2\sqrt{7}$$

Iffattura 27=3^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{2\sqrt{3}}{3}+\frac{12}{3\sqrt{3}}+2\sqrt{7}$$

Irrazzjonalizza d-denominatur tal-\frac{12}{3\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{2\sqrt{3}}{3}+\frac{12\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}+2\sqrt{7}$$

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

$$\frac{2\sqrt{3}}{3}+\frac{12\sqrt{3}}{3\times 3}+2\sqrt{7}$$

Annulla 3 fin-numeratur u d-denominatur.

$$\frac{2\sqrt{3}}{3}+\frac{4\sqrt{3}}{3}+2\sqrt{7}$$

Ikkombina \frac{2\sqrt{3}}{3} u \frac{4\sqrt{3}}{3} biex tikseb 2\sqrt{3}.

$$2\sqrt{3}+2\sqrt{7}$$

Fattur

$$2 {(\sqrt{3} + \sqrt{7})} = 8.755604237$$