Issolvi 8/sqrt{4-sqrt{2}}

$$\frac{ 8 }{ \sqrt{ 4 } - \sqrt{ 2 } }$$

Evalwa

$$4\sqrt{2}+8\approx 13.656854249$$

Passi tas-Soluzzjonijiet

Ikkalkula l-għerq kwadrat ta' 4 u ikseb 2.

$$\frac{8}{2-\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{8}{2-\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-2+\sqrt{2}.

$$\frac{8\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}$$

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

$$\frac{8\left(2+\sqrt{2}\right)}{2^{2}-\left(\sqrt{2}\right)^{2}}$$

Ikkwadra 2. Ikkwadra \sqrt{2}.

$$\frac{8\left(2+\sqrt{2}\right)}{4-2}$$

Naqqas 2 minn 4 biex tikseb 2.

$$\frac{8\left(2+\sqrt{2}\right)}{2}$$

Iddividi 8\left(2+\sqrt{2}\right) b'2 biex tikseb4\left(2+\sqrt{2}\right).

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

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

$$8+4\sqrt{2}$$