Solve -1^2020-sqrt{8}+(1/2)^-1+(sqrt{3}-sqrt{2})^0

$$- 1 ^ { 2020 } - \sqrt { 8 } + ( \frac { 1 } { 2 } ) ^ { - 1 } + ( \sqrt { 3 } - \sqrt { 2 } ) ^ { 0 }$$

Evaluate

$$2-2\sqrt{2}\approx -0.828427125$$

Solution Steps

Calculate 1 to the power of 2020 and get 1.

$$-1-\sqrt{8}+\left(\frac{1}{2}\right)^{-1}+\left(\sqrt{3}-\sqrt{2}\right)^{0}$$

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}.

$$-1-2\sqrt{2}+\left(\frac{1}{2}\right)^{-1}+\left(\sqrt{3}-\sqrt{2}\right)^{0}$$

Calculate \frac{1}{2} to the power of -1 and get 2.

$$-1-2\sqrt{2}+2+\left(\sqrt{3}-\sqrt{2}\right)^{0}$$

Add -1 and 2 to get 1.

$$1-2\sqrt{2}+\left(\sqrt{3}-\sqrt{2}\right)^{0}$$

Calculate \sqrt{3}-\sqrt{2} to the power of 0 and get 1.

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

Add 1 and 1 to get 2.

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