Issolvi 3/sqrt{5+sqrt{2}}+1/3+sqrt{8}

$$\frac { 3 } { \sqrt { 5 } + \sqrt { 2 } } + \frac { 1 } { 3 + \sqrt { 8 } }$$

Evalwa

$$\sqrt{5}+3-3\sqrt{2}\approx 0.99342729$$

Passi tas-Soluzzjonijiet

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

$$\frac{3\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)}+\frac{1}{3+\sqrt{8}}$$

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

$$\frac{3\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}}+\frac{1}{3+\sqrt{8}}$$

Ikkwadra \sqrt{5}. Ikkwadra \sqrt{2}.

$$\frac{3\left(\sqrt{5}-\sqrt{2}\right)}{5-2}+\frac{1}{3+\sqrt{8}}$$

Naqqas 2 minn 5 biex tikseb 3.

$$\frac{3\left(\sqrt{5}-\sqrt{2}\right)}{3}+\frac{1}{3+\sqrt{8}}$$

Annulla 3 u 3.

$$\sqrt{5}-\sqrt{2}+\frac{1}{3+\sqrt{8}}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\sqrt{5}-\sqrt{2}+\frac{1}{3+2\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{3+2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-3-2\sqrt{2}.

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

Ikkunsidra li \left(3+2\sqrt{2}\right)\left(3-2\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}.

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

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{9-\left(2\sqrt{2}\right)^{2}}$$

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

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{9-2^{2}\left(\sqrt{2}\right)^{2}}$$

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

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{9-4\left(\sqrt{2}\right)^{2}}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{9-4\times 2}$$

Immultiplika 4 u 2 biex tikseb 8.

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{9-8}$$

Naqqas 8 minn 9 biex tikseb 1.

$$\sqrt{5}-\sqrt{2}+\frac{3-2\sqrt{2}}{1}$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

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

Ikkombina -\sqrt{2} u -2\sqrt{2} biex tikseb -3\sqrt{2}.

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