Issolvi 7/5-2sqrt{6}

$$\frac { 7 } { 5 - 2 \sqrt { 6 } }$$

Evalwa

$$14\sqrt{6}+35\approx 69.292856399$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{7}{5-2\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-5+2\sqrt{6}.

$$\frac{7\left(5+2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)}$$

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}.

$$\frac{7\left(5+2\sqrt{6}\right)}{5^{2}-\left(-2\sqrt{6}\right)^{2}}$$

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

$$\frac{7\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}}$$

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

$$\frac{7\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{7\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{7\left(5+2\sqrt{6}\right)}{25-4\times 6}$$

Immultiplika 4 u 6 biex tikseb 24.

$$\frac{7\left(5+2\sqrt{6}\right)}{25-24}$$

Naqqas 24 minn 25 biex tikseb 1.

$$\frac{7\left(5+2\sqrt{6}\right)}{1}$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$7\left(5+2\sqrt{6}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 7 b'5+2\sqrt{6}.

$$35+14\sqrt{6}$$