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

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

Evaluate

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

Solution Steps

Calculate 2 to the power of 3 and get 8.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Combine \sqrt{3} and -\sqrt{3} to get 0.

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

Combine -4\sqrt{2} and -\sqrt{2} to get -5\sqrt{2}.

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

Use the distributive property to multiply -2 by 2+2\sqrt{6}-5\sqrt{2}.

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

Subtract 4 from 8 to get 4.

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

Factor

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