Issolvi 1/3-sqrt{8}-2sqrt{2}+6

$$\frac { 1 } { 3 - \sqrt { 8 } } - 2 \sqrt { 2 } + 6$$

Evalwa

$$9$$

Passi tas-Soluzzjonijiet

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}.

$$\frac{1}{3-2\sqrt{2}}-2\sqrt{2}+6$$

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

$$\frac{3+2\sqrt{2}}{\left(3-2\sqrt{2}\right)\left(3+2\sqrt{2}\right)}-2\sqrt{2}+6$$

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}.

$$\frac{3+2\sqrt{2}}{3^{2}-\left(-2\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

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

$$\frac{3+2\sqrt{2}}{9-\left(-2\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

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

$$\frac{3+2\sqrt{2}}{9-\left(-2\right)^{2}\left(\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

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

$$\frac{3+2\sqrt{2}}{9-4\left(\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

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

$$\frac{3+2\sqrt{2}}{9-4\times 2}-2\sqrt{2}+6$$

Immultiplika 4 u 2 biex tikseb 8.

$$\frac{3+2\sqrt{2}}{9-8}-2\sqrt{2}+6$$

Naqqas 8 minn 9 biex tikseb 1.

$$\frac{3+2\sqrt{2}}{1}-2\sqrt{2}+6$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$3+2\sqrt{2}-2\sqrt{2}+6$$

Ikkombina 2\sqrt{2} u -2\sqrt{2} biex tikseb 0.

$$3+6$$

Żid 3 u 6 biex tikseb 9.

$$9$$

Fattur

$$3^{2}$$