Issolvi frac{sqrt{3}}{sqrt{5}-sqrt{2}}

$$\frac { \sqrt { 3 } } { \sqrt { 5 } - \sqrt { 2 } }$$

Evalwa

$$\frac{\sqrt{6}+\sqrt{15}}{3}\approx 2.10749103$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{3}}{\sqrt{5}-\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}+\sqrt{2}.

$$\frac{\sqrt{3}\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}$$

Ikkunsidra li \left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\sqrt{3}\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Ikkwadra \sqrt{5}. Ikkwadra \sqrt{2}.

$$\frac{\sqrt{3}\left(\sqrt{5}+\sqrt{2}\right)}{5-2}$$

Naqqas 2 minn 5 biex tikseb 3.

$$\frac{\sqrt{3}\left(\sqrt{5}+\sqrt{2}\right)}{3}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{3} b'\sqrt{5}+\sqrt{2}.

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

Biex timmultiplika \sqrt{3} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{15}+\sqrt{3}\sqrt{2}}{3}$$

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

$$\frac{\sqrt{15}+\sqrt{6}}{3}$$