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

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

Evalwa

$$\frac{-\sqrt{6}-\sqrt{10}}{2}\approx -2.805883701$$

Passi tas-Soluzzjonijiet

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

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

Ikkunsidra li \left(\sqrt{3}-\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\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}.

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

Ikkwadra \sqrt{3}. Ikkwadra \sqrt{5}.

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

Naqqas 5 minn 3 biex tikseb -2.

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

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

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

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

$$\frac{\sqrt{6}+\sqrt{2}\sqrt{5}}{-2}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{6}+\sqrt{10}}{-2}$$

Immultiplika kemm in-numeratur u d-denominatur b'i.

$$\frac{-\sqrt{6}-\sqrt{10}}{2}$$