Datrys {left(sqrt{6}+sqrt{2}right)}^2-2sqrt{2}*sqrt{6}+sqrt{2}

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

Enrhifo

$$\sqrt{2}+8\approx 9.414213562$$

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}.

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

Sgwâr \sqrt{6} yw 6.

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

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

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

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

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

Lluosi 2 a 2 i gael 4.

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

Sgwâr \sqrt{2} yw 2.

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

Adio 6 a 2 i gael 8.

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

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

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

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

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

Lluosi 2 a 2 i gael 4.

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

Cyfuno 4\sqrt{3} a -4\sqrt{3} i gael 0.

$$8+\sqrt{2}$$