Issolvi frac{2sqrt{3}-sqrt{2}}{2sqrt{3}+sqrt{3}}

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

Evalwa

$$-\frac{\sqrt{6}}{9}+\frac{2}{3}\approx 0.39450114$$

Passi tas-Soluzzjonijiet

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

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

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

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

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

$$\frac{\left(2\sqrt{3}-\sqrt{2}\right)\sqrt{3}}{3\times 3}$$

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{\left(2\sqrt{3}-\sqrt{2}\right)\sqrt{3}}{9}$$

Uża l-propjetà distributtiva biex timmultiplika 2\sqrt{3}-\sqrt{2} b'\sqrt{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}-\sqrt{2}\sqrt{3}}{9}$$

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

$$\frac{2\times 3-\sqrt{2}\sqrt{3}}{9}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6-\sqrt{2}\sqrt{3}}{9}$$

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{6-\sqrt{6}}{9}$$

Fattur

$$\frac{\sqrt{6} {(\sqrt{6} - 1)}}{9} = 0.3945011396907579$$