Datrys {l}{(1/3sqrt{27}-sqrt{24}}{-3sqrt{2/3})*sqrt{12}}

$$\left. \begin{array} { l } { ( \frac { 1 } { 3 } \sqrt { 27 } - \sqrt { 24 } } \\ { - 3 \sqrt { \frac { 2 } { 3 } } ) \times \sqrt { 12 } } \end{array} \right.$$

Enrhifo

$$6-18\sqrt{2}\approx -19.455844123$$

Camau Ateb

Ffactora 27=3^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 3} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{3}. Cymryd isradd 3^{2}.

$$\left(\frac{1}{3}\times 3\sqrt{3}-\sqrt{24}-3\sqrt{\frac{2}{3}}\right)\sqrt{12}$$

Canslo 3 a 3.

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

Ffactora 24=2^{2}\times 6. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 6} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{6}. Cymryd isradd 2^{2}.

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

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{2}{3}} fel rhaniad ail israddau \frac{\sqrt{2}}{\sqrt{3}}.

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

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

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

Sgwâr \sqrt{3} yw 3.

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

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

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

Canslo 3 a 3.

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

Cyfuno -2\sqrt{6} a -\sqrt{6} i gael -3\sqrt{6}.

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

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}.

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

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

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

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

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

Sgwâr \sqrt{3} yw 3.

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

Lluosi 2 a 3 i gael 6.

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

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

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

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

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

Lluosi -6 a 3 i gael -18.

$$6-18\sqrt{2}$$

Ffactor

$$6 {(1 - 3 \sqrt{2})} = -19.455844123$$