Datrys frac{left(sqrt{6}-sqrt{12}right)*sqrt{3}}{sqrt{6}}+sqrt{6}

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

Enrhifo

$$\sqrt{3}\approx 1.732050808$$

Camau Ateb

Ffactora 12=2^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 3} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{3}. Cymryd isradd 2^{2}.

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

Mae'n rhesymoli enwadur \frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{6}.

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

Sgwâr \sqrt{6} yw 6.

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

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

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

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

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

Rhannu \left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2} â 6 i gael \left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}.

$$\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}+\sqrt{6}$$

Defnyddio’r briodwedd ddosbarthu i luosi \sqrt{6}-2\sqrt{3} â \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-2\sqrt{3}\times \frac{1}{2}\right)\sqrt{2}+\sqrt{6}$$

Lluoswch -2 â \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-\sqrt{3}\right)\sqrt{2}+\sqrt{6}$$

Defnyddio’r briodwedd ddosbarthu i luosi \sqrt{6}\times \frac{1}{2}-\sqrt{3} â \sqrt{2}.

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

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

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

Lluosi \sqrt{2} a \sqrt{2} i gael 2.

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

Canslo 2 a 2.

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

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

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

Cyfuno -\sqrt{6} a \sqrt{6} i gael 0.

$$\sqrt{3}$$