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

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

Luacháil

$$10\sqrt{2}+4-4\sqrt{6}\approx 8.344176653$$

Céimeanna Réitigh

Ríomh cumhacht 2 de 3 agus faigh 8.

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

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{3} a iolrú.

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

Fachtóirigh 32=4^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{2}. Tóg fréamh chearnach 4^{2}.

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

Comhcheangail \sqrt{3} agus -\sqrt{3} chun 0 a fháil.

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

Comhcheangail -4\sqrt{2} agus -\sqrt{2} chun -5\sqrt{2} a fháil.

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

Úsáid an t-airí dáileach chun -2 a mhéadú faoi 2+2\sqrt{6}-5\sqrt{2}.

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

Dealaigh 4 ó 8 chun 4 a fháil.

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

Fachtóirigh

$$2 {(5 \sqrt{2} + 2 - 2 \sqrt{6})} = 8.344176653$$