Lahenda (sqrt{10}-sqrt{2})^2

$$( \sqrt { 10 } - \sqrt { 2 } ) ^ { 2 }$$

Arvuta

$$12-4\sqrt{5}\approx 3,05572809$$

Lahenduse etapid

Kasutage kaksliikme \left(\sqrt{10}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$\left(\sqrt{10}\right)^{2}-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

\sqrt{10} ruut on 10.

$$10-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

Tegurda 10=2\times 5. Kirjutage \sqrt{2\times 5} toote juured, kui see ruut \sqrt{2}\sqrt{5}.

$$10-2\sqrt{2}\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

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

$$10-2\times 2\sqrt{5}+\left(\sqrt{2}\right)^{2}$$

Korrutage -2 ja 2, et leida -4.

$$10-4\sqrt{5}+\left(\sqrt{2}\right)^{2}$$

\sqrt{2} ruut on 2.

$$10-4\sqrt{5}+2$$

Liitke 10 ja 2, et leida 12.

$$12-4\sqrt{5}$$

Laienda

$$12-4\sqrt{5}$$

Lahenduse etapid

Kasutage kaksliikme \left(\sqrt{10}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$\left(\sqrt{10}\right)^{2}-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

\sqrt{10} ruut on 10.

$$10-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

Tegurda 10=2\times 5. Kirjutage \sqrt{2\times 5} toote juured, kui see ruut \sqrt{2}\sqrt{5}.

$$10-2\sqrt{2}\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}$$

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

$$10-2\times 2\sqrt{5}+\left(\sqrt{2}\right)^{2}$$

Korrutage -2 ja 2, et leida -4.

$$10-4\sqrt{5}+\left(\sqrt{2}\right)^{2}$$

\sqrt{2} ruut on 2.

$$10-4\sqrt{5}+2$$

Liitke 10 ja 2, et leida 12.

$$12-4\sqrt{5}$$