Issolvi sqrt{8}div(sqrt{2}-1)

$$\sqrt { 8 } \div ( \sqrt { 2 } - 1 )$$

Evalwa

$$2\sqrt{2}+4\approx 6.828427125$$

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}.

$$\frac{2\sqrt{2}}{\sqrt{2}-1}$$

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

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

Ikkunsidra li \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\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}.

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

Ikkwadra \sqrt{2}. Ikkwadra 1.

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

Naqqas 1 minn 2 biex tikseb 1.

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

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$2\sqrt{2}\left(\sqrt{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2\sqrt{2} b'\sqrt{2}+1.

$$2\left(\sqrt{2}\right)^{2}+2\sqrt{2}$$

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

$$2\times 2+2\sqrt{2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$4+2\sqrt{2}$$