Issolvi frac{sqrt{12}}{sqrt{2}-1}

$$\frac { \sqrt { 12 } } { \sqrt { 2 } - 1 }$$

Evalwa

$$2\sqrt{3}\left(\sqrt{2}+1\right)\approx 8.363081101$$

Passi tas-Soluzzjonijiet

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

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

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

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

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}.

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

Ikkwadra \sqrt{2}. Ikkwadra 1.

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

Naqqas 1 minn 2 biex tikseb 1.

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

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$2\sqrt{3}\left(\sqrt{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2\sqrt{3} b'\sqrt{2}+1.

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

Biex timmultiplika \sqrt{3} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

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