Issolvi frac{sqrt{6}+3sqrt{3}}{sqrt{3}}

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

Evalwa

$$\sqrt{2}+3\approx 4.414213562$$

Passi tas-Soluzzjonijiet

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

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

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

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

Uża l-propjetà distributtiva biex timmultiplika \sqrt{6}+3\sqrt{3} b'\sqrt{3}.

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

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}.

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

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

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

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

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

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{3\sqrt{2}+9}{3}$$

Iddividi kull terminu ta' 3\sqrt{2}+9 b'3 biex tikseb\sqrt{2}+3.

$$\sqrt{2}+3$$