Issolvi 2/5-sqrt{3}

$$\frac{ 2 }{ 5- \sqrt{ 3 } }$$

Evalwa

$$\frac{\sqrt{3}+5}{11}\approx 0.612004619$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{2}{5-\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-5+\sqrt{3}.

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

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

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

Ikkwadra 5. Ikkwadra \sqrt{3}.

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

Naqqas 3 minn 25 biex tikseb 22.

$$\frac{2\left(5+\sqrt{3}\right)}{22}$$

Iddividi 2\left(5+\sqrt{3}\right) b'22 biex tikseb\frac{1}{11}\left(5+\sqrt{3}\right).

$$\frac{1}{11}\left(5+\sqrt{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{11} b'5+\sqrt{3}.

$$\frac{1}{11}\times 5+\frac{1}{11}\sqrt{3}$$

Immultiplika \frac{1}{11} u 5 biex tikseb \frac{5}{11}.

$$\frac{5}{11}+\frac{1}{11}\sqrt{3}$$