Issolvi =frac{12sqrt{3}+24}{sqrt{2}+sqrt{6}}

$$= \frac { 12 \sqrt { 3 } + 24 } { \sqrt { 2 } + \sqrt { 6 } }$$

Evalwa

$$3\left(\sqrt{2}+\sqrt{6}\right)\approx 11.591109915$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{12\sqrt{3}+24}{\sqrt{2}+\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}-\sqrt{6}.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right)}$$

Ikkunsidra li \left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\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}.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{6}\right)^{2}}$$

Ikkwadra \sqrt{2}. Ikkwadra \sqrt{6}.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{2-6}$$

Naqqas 6 minn 2 biex tikseb -4.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{-4}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 12\sqrt{3}+24 b'kull terminu ta' \sqrt{2}-\sqrt{6}.

$$\frac{12\sqrt{3}\sqrt{2}-12\sqrt{3}\sqrt{6}+24\sqrt{2}-24\sqrt{6}}{-4}$$

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

$$\frac{12\sqrt{6}-12\sqrt{3}\sqrt{6}+24\sqrt{2}-24\sqrt{6}}{-4}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

$$\frac{12\sqrt{6}-12\sqrt{3}\sqrt{3}\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$\frac{12\sqrt{6}-12\times 3\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

Immultiplika -12 u 3 biex tikseb -36.

$$\frac{12\sqrt{6}-36\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

Ikkombina -36\sqrt{2} u 24\sqrt{2} biex tikseb -12\sqrt{2}.

$$\frac{12\sqrt{6}-12\sqrt{2}-24\sqrt{6}}{-4}$$

Ikkombina 12\sqrt{6} u -24\sqrt{6} biex tikseb -12\sqrt{6}.

$$\frac{-12\sqrt{6}-12\sqrt{2}}{-4}$$

Fattur

$$3 {(\sqrt{2} + \sqrt{6})} = 11.591109915$$