Issolvi 5sqrt{3}+2sqrt{27}+1/sqrt{3}

$$5 \sqrt{ 3 } +2 \sqrt{ 27 } + \frac{ 1 }{ \sqrt{ 3 } }$$

Evalwa

$$\frac{34\sqrt{3}}{3}\approx 19.629909152$$

Passi tas-Soluzzjonijiet

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}.

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

Immultiplika 2 u 3 biex tikseb 6.

$$5\sqrt{3}+6\sqrt{3}+\frac{1}{\sqrt{3}}$$

Ikkombina 5\sqrt{3} u 6\sqrt{3} biex tikseb 11\sqrt{3}.

$$11\sqrt{3}+\frac{1}{\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$11\sqrt{3}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

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

$$11\sqrt{3}+\frac{\sqrt{3}}{3}$$

Ikkombina 11\sqrt{3} u \frac{\sqrt{3}}{3} biex tikseb \frac{34}{3}\sqrt{3}.

$$\frac{34}{3}\sqrt{3}$$