Réitigh (10sqrt{6}+10sqrt{2})^2

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

Luacháil

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

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(10\sqrt{6}+10\sqrt{2}\right)^{2} a leathnú.

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

Is é 6 uimhir chearnach \sqrt{6}.

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

Méadaigh 100 agus 6 chun 600 a fháil.

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

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

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

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

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

Méadaigh 200 agus 2 chun 400 a fháil.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 100 agus 2 chun 200 a fháil.

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

Suimigh 600 agus 200 chun 800 a fháil.

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

Fairsingigh

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

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(10\sqrt{6}+10\sqrt{2}\right)^{2} a leathnú.

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

Is é 6 uimhir chearnach \sqrt{6}.

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

Méadaigh 100 agus 6 chun 600 a fháil.

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

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

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

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

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

Méadaigh 200 agus 2 chun 400 a fháil.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 100 agus 2 chun 200 a fháil.

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

Suimigh 600 agus 200 chun 800 a fháil.

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