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

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

Arvuta

$$400\left(\sqrt{3}+2\right)\approx 1492,820323028$$

Lahenduse etapid

Kasutage kaksliikme \left(10\sqrt{6}+10\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

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

\sqrt{6} ruut on 6.

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

Korrutage 100 ja 6, et leida 600.

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

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

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

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

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

Korrutage 200 ja 2, et leida 400.

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

\sqrt{2} ruut on 2.

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

Korrutage 100 ja 2, et leida 200.

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

Liitke 600 ja 200, et leida 800.

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

Laienda

$$400 \sqrt{3} + 800 = 1492,820323028$$

Lahenduse etapid

Kasutage kaksliikme \left(10\sqrt{6}+10\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

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

\sqrt{6} ruut on 6.

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

Korrutage 100 ja 6, et leida 600.

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

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

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

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

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

Korrutage 200 ja 2, et leida 400.

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

\sqrt{2} ruut on 2.

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

Korrutage 100 ja 2, et leida 200.

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

Liitke 600 ja 200, et leida 800.

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