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

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

Arvuta

$$\sqrt{2}+8\approx 9,414213562$$

Lahenduse etapid

Kasutage kaksliikme \left(\sqrt{6}+\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

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

\sqrt{6} ruut on 6.

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

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Korrutage 2 ja 2, et leida 4.

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

\sqrt{2} ruut on 2.

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

Liitke 6 ja 2, et leida 8.

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

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Korrutage 2 ja 2, et leida 4.

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

Kombineerige 4\sqrt{3} ja -4\sqrt{3}, et leida 0.

$$8+\sqrt{2}$$