Issolvi frac{sqrt{2}}{4-sqrt{3}}

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

Evalwa

$$\frac{\sqrt{2}\left(\sqrt{3}+4\right)}{13}\approx 0.623564922$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{4-\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-4+\sqrt{3}.

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

Ikkunsidra li \left(4-\sqrt{3}\right)\left(4+\sqrt{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}.

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

Ikkwadra 4. Ikkwadra \sqrt{3}.

$$\frac{\sqrt{2}\left(4+\sqrt{3}\right)}{16-3}$$

Naqqas 3 minn 16 biex tikseb 13.

$$\frac{\sqrt{2}\left(4+\sqrt{3}\right)}{13}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{2} b'4+\sqrt{3}.

$$\frac{4\sqrt{2}+\sqrt{2}\sqrt{3}}{13}$$

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

$$\frac{4\sqrt{2}+\sqrt{6}}{13}$$