Solve sqrt{8}-(1/2)^-2+(2-sqrt{3})^0-sqrt{12}

$$\sqrt { 8 } - ( \frac { 1 } { 2 } ) ^ { - 2 } + ( 2 - \sqrt { 3 } ) ^ { 0 } - \sqrt { 12 }$$

Evaluate

$$2\sqrt{2}-2\sqrt{3}-3\approx -3.63567449$$

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}.

$$2\sqrt{2}-\left(\frac{1}{2}\right)^{-2}+\left(2-\sqrt{3}\right)^{0}-\sqrt{12}$$

Calculate \frac{1}{2} to the power of -2 and get 4.

$$2\sqrt{2}-4+\left(2-\sqrt{3}\right)^{0}-\sqrt{12}$$

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

$$2\sqrt{2}-4+1-\sqrt{12}$$

Add -4 and 1 to get -3.

$$2\sqrt{2}-3-\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{2}-3-2\sqrt{3}$$