Datrys (10sqrt{6}+10sqrt{2})^2

$$( 10 \sqrt { 6 } + 10 \sqrt { 2 } ) ^ { 2 }$$

Enrhifo

$$400\left(\sqrt{3}+2\right)\approx 1492.820323028$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Sgwâr \sqrt{6} yw 6.

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Lluosi 100 a 6 i gael 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Lluosi 200 a 2 i gael 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Sgwâr \sqrt{2} yw 2.

$$600+400\sqrt{3}+100\times 2$$

Lluosi 100 a 2 i gael 200.

$$600+400\sqrt{3}+200$$

Adio 600 a 200 i gael 800.

$$800+400\sqrt{3}$$

Ehangu

$$400 \sqrt{3} + 800 = 1492.820323028$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Sgwâr \sqrt{6} yw 6.

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Lluosi 100 a 6 i gael 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Lluosi 200 a 2 i gael 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Sgwâr \sqrt{2} yw 2.

$$600+400\sqrt{3}+100\times 2$$

Lluosi 100 a 2 i gael 200.

$$600+400\sqrt{3}+200$$

Adio 600 a 200 i gael 800.

$$800+400\sqrt{3}$$