Lahenda 2^3-2(2+sqrt{3}+sqrt{2}*2sqrt{3}-sqrt{32}-sqrt{3}-sqrt{2})

$$2 ^ { 3 } - 2 ( 2 + \sqrt { 3 } + \sqrt { 2 } \cdot 2 \sqrt { 3 } - \sqrt { 32 } - \sqrt { 3 } - \sqrt { 2 } )$$

Arvuta

$$10\sqrt{2}+4-4\sqrt{6}\approx 8,344176653$$

Lahenduse etapid

Arvutage 3 aste 2 ja leidke 8.

$$8-2\left(2+\sqrt{3}+2\sqrt{2}\sqrt{3}-\sqrt{32}-\sqrt{3}-\sqrt{2}\right)$$

\sqrt{2} ja \sqrt{3} korrutage numbrid, mis on sama juur.

$$8-2\left(2+\sqrt{3}+2\sqrt{6}-\sqrt{32}-\sqrt{3}-\sqrt{2}\right)$$

Tegurda 32=4^{2}\times 2. Kirjutage \sqrt{4^{2}\times 2} toote juured, kui see ruut \sqrt{4^{2}}\sqrt{2}. Leidke 4^{2} ruutjuur.

$$8-2\left(2+\sqrt{3}+2\sqrt{6}-4\sqrt{2}-\sqrt{3}-\sqrt{2}\right)$$

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

$$8-2\left(2+2\sqrt{6}-4\sqrt{2}-\sqrt{2}\right)$$

Kombineerige -4\sqrt{2} ja -\sqrt{2}, et leida -5\sqrt{2}.

$$8-2\left(2+2\sqrt{6}-5\sqrt{2}\right)$$

Kasutage distributiivsusomadust, et korrutada -2 ja 2+2\sqrt{6}-5\sqrt{2}.

$$8-4-4\sqrt{6}+10\sqrt{2}$$

Lahutage 4 väärtusest 8, et leida 4.

$$4-4\sqrt{6}+10\sqrt{2}$$

Lahuta teguriteks

$$2 {(5 \sqrt{2} + 2 - 2 \sqrt{6})} = 8,344176653$$