Datrys (sqrt{6}-sqrt{2})^2-frac{sqrt{6}-sqrt{2}}{sqrt{6}+sqrt{2}}

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

Enrhifo

$$6-3\sqrt{3}\approx 0.803847577$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(\sqrt{6}-\sqrt{2}\right)^{2}.

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

Sgwâr \sqrt{6} yw 6.

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

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

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

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

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

Lluosi -2 a 2 i gael -4.

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

Sgwâr \sqrt{2} yw 2.

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

Adio 6 a 2 i gael 8.

$$8-4\sqrt{3}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

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

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}$$

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

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{6}. Sgwâr \sqrt{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{6-2}$$

Tynnu 2 o 6 i gael 4.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{4}$$

Lluosi \sqrt{6}-\sqrt{2} a \sqrt{6}-\sqrt{2} i gael \left(\sqrt{6}-\sqrt{2}\right)^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)^{2}}{4}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(\sqrt{6}-\sqrt{2}\right)^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}\right)^{2}-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

Sgwâr \sqrt{6} yw 6.

$$8-4\sqrt{3}-\frac{6-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

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

$$8-4\sqrt{3}-\frac{6-2\sqrt{2}\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

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

$$8-4\sqrt{3}-\frac{6-2\times 2\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

Lluosi -2 a 2 i gael -4.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

Sgwâr \sqrt{2} yw 2.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+2}{4}$$

Adio 6 a 2 i gael 8.

$$8-4\sqrt{3}-\frac{8-4\sqrt{3}}{4}$$

Rhannu pob term 8-4\sqrt{3} â 4 i gael 2-\sqrt{3}.

$$8-4\sqrt{3}-\left(2-\sqrt{3}\right)$$

I ddod o hyd i wrthwyneb 2-\sqrt{3}, dewch o hyd i wrthwyneb pob term.

$$8-4\sqrt{3}-2+\sqrt{3}$$

Tynnu 2 o 8 i gael 6.

$$6-4\sqrt{3}+\sqrt{3}$$

Cyfuno -4\sqrt{3} a \sqrt{3} i gael -3\sqrt{3}.

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

Ffactor

$$3 {(2 - \sqrt{3})} = 0.803847577$$