Issolvi 14/5sqrt{3-sqrt{5}}

$$\frac{ 14 }{ 5 \sqrt{ 3 } - \sqrt{ 5 } }$$

Evalwa

$$\frac{\sqrt{5}\left(\sqrt{15}+1\right)}{5}\approx 2.179264403$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{14}{5\sqrt{3}-\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-5\sqrt{3}+\sqrt{5}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right)}$$

Ikkunsidra li \left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\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}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Espandi \left(5\sqrt{3}\right)^{2}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\times 3-\left(\sqrt{5}\right)^{2}}$$

Immultiplika 25 u 3 biex tikseb 75.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-\left(\sqrt{5}\right)^{2}}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-5}$$

Naqqas 5 minn 75 biex tikseb 70.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{70}$$

Iddividi 14\left(5\sqrt{3}+\sqrt{5}\right) b'70 biex tikseb\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right).

$$\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{5} b'5\sqrt{3}+\sqrt{5}.

$$\frac{1}{5}\times 5\sqrt{3}+\frac{1}{5}\sqrt{5}$$

Annulla 5 u 5.

$$\sqrt{3}+\frac{1}{5}\sqrt{5}$$