Datrys frac{sqrt{75}-sqrt{18}}{sqrt{12}}

$$\frac { \sqrt { 75 } - \sqrt { 18 } } { \sqrt { 12 } }$$

Enrhifo

$$\frac{5-\sqrt{6}}{2}\approx 1.275255129$$

Camau Ateb

Ffactora 75=5^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 3} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{3}. Cymryd isradd 5^{2}.

$$\frac{5\sqrt{3}-\sqrt{18}}{\sqrt{12}}$$

Ffactora 18=3^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 2} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{2}. Cymryd isradd 3^{2}.

$$\frac{5\sqrt{3}-3\sqrt{2}}{\sqrt{12}}$$

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}.

$$\frac{5\sqrt{3}-3\sqrt{2}}{2\sqrt{3}}$$

Mae'n rhesymoli enwadur \frac{5\sqrt{3}-3\sqrt{2}}{2\sqrt{3}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{3}.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

Sgwâr \sqrt{3} yw 3.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{2\times 3}$$

Lluosi 2 a 3 i gael 6.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{6}$$

Defnyddio’r briodwedd ddosbarthu i luosi 5\sqrt{3}-3\sqrt{2} â \sqrt{3}.

$$\frac{5\left(\sqrt{3}\right)^{2}-3\sqrt{2}\sqrt{3}}{6}$$

Sgwâr \sqrt{3} yw 3.

$$\frac{5\times 3-3\sqrt{2}\sqrt{3}}{6}$$

Lluosi 5 a 3 i gael 15.

$$\frac{15-3\sqrt{2}\sqrt{3}}{6}$$

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

$$\frac{15-3\sqrt{6}}{6}$$