Solve sqrt{8}+(-1)^3-2*frac{sqrt{2}}{2}=

$$\sqrt { 8 } + ( - 1 ) ^ { 3 } - 2 \times \frac { \sqrt { 2 } } { 2 } =$$

Evaluate

$$\sqrt{2}-1\approx 0.414213562$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\left(-1\right)^{3}-2\times \frac{\sqrt{2}}{2}$$

Calculate -1 to the power of 3 and get -1.

$$2\sqrt{2}-1-2\times \frac{\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$2\sqrt{2}-1-\sqrt{2}$$

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

$$\sqrt{2}-1$$