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

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

Enrhifo

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

Camau Ateb

Mae'n rhesymoli enwadur \frac{12\sqrt{3}+24}{\sqrt{2}+\sqrt{6}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}-\sqrt{6}.

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

Ystyriwch \left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Sgwâr \sqrt{2}. Sgwâr \sqrt{6}.

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

Tynnu 6 o 2 i gael -4.

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

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 12\sqrt{3}+24 gan bob \sqrt{2}-\sqrt{6}.

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

I luosi \sqrt{3} a \sqrt{2}, dylid lluosi'r rhifau dan yr ail isradd.

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

Ffactora 6=3\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3\times 2} fel lluoswm ail israddau \sqrt{3}\sqrt{2}.

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

Lluosi \sqrt{3} a \sqrt{3} i gael 3.

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

Lluosi -12 a 3 i gael -36.

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

Cyfuno -36\sqrt{2} a 24\sqrt{2} i gael -12\sqrt{2}.

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

Cyfuno 12\sqrt{6} a -24\sqrt{6} i gael -12\sqrt{6}.

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

Ffactor

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