Issolvi 20/sqrt{6-sqrt{2}}

$$\frac{ 20 }{ \sqrt{ 6 } - \sqrt{ 2 } }$$

Evalwa

$$5\left(\sqrt{2}+\sqrt{6}\right)\approx 19.318516526$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{20}{\sqrt{6}-\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}+\sqrt{2}.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}+\sqrt{2}\right)}$$

Ikkunsidra li \left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}+\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}.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Ikkwadra \sqrt{6}. Ikkwadra \sqrt{2}.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{6-2}$$

Naqqas 2 minn 6 biex tikseb 4.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{4}$$

Iddividi 20\left(\sqrt{6}+\sqrt{2}\right) b'4 biex tikseb5\left(\sqrt{6}+\sqrt{2}\right).

$$5\left(\sqrt{6}+\sqrt{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5 b'\sqrt{6}+\sqrt{2}.

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