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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Ikkalkula 2 bil-power ta' 3 u tikseb 8.

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

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

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

Iffattura 32=4^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 4^{2}.

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

Ikkombina \sqrt{3} u -\sqrt{3} biex tikseb 0.

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

Ikkombina -4\sqrt{2} u -\sqrt{2} biex tikseb -5\sqrt{2}.

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

Uża l-propjetà distributtiva biex timmultiplika -2 b'2+2\sqrt{6}-5\sqrt{2}.

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

Naqqas 4 minn 8 biex tikseb 4.

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

Fattur

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