Issolvi frac{2sqrt{2}}{5-2sqrt{6}}

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

Evalwa

$$8\sqrt{3}+10\sqrt{2}\approx 27.998542084$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{2}}{5-2\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-5+2\sqrt{6}.

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

Ikkunsidra li \left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\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}.

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

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}}$$

Espandi \left(-2\sqrt{6}\right)^{2}.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

Ikkalkula -2 bil-power ta' 2 u tikseb 4.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\times 6}$$

Immultiplika 4 u 6 biex tikseb 24.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-24}$$

Naqqas 24 minn 25 biex tikseb 1.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{1}$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

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

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

$$10\sqrt{2}+4\sqrt{2}\sqrt{6}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

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

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$10\sqrt{2}+4\times 2\sqrt{3}$$

Immultiplika 4 u 2 biex tikseb 8.

$$10\sqrt{2}+8\sqrt{3}$$