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

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

Evalwa

$$-\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{4}\approx 0.270090757$$

Passi tas-Soluzzjonijiet

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

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

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

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

Ikkwadra \sqrt{5}. Ikkwadra 3.

$$\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{5-9}$$

Naqqas 9 minn 5 biex tikseb -4.

$$\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{-4}$$

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

$$\frac{\sqrt{2}\sqrt{5}-3\sqrt{2}}{-4}$$

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

$$\frac{\sqrt{10}-3\sqrt{2}}{-4}$$

Immultiplika kemm in-numeratur u kif ukoll id-denominatur b’-1.

$$\frac{-\sqrt{10}+3\sqrt{2}}{4}$$