Solve (3-x)^0-sqrt{8}+(1/2)^-1-|-4|

$$( 3 - x ) ^ { 0 } - \sqrt { 8 } + ( \frac { 1 } { 2 } ) ^ { - 1 } - | - 4 |$$

Evaluate

$$-2\sqrt{2}-1\approx -3.828427125$$

Solution Steps

Calculate 3-x to the power of 0 and get 1.

$$1-\sqrt{8}+\left(\frac{1}{2}\right)^{-1}-|-4|$$

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}.

$$1-2\sqrt{2}+\left(\frac{1}{2}\right)^{-1}-|-4|$$

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

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

Add 1 and 2 to get 3.

$$3-2\sqrt{2}-|-4|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$3-2\sqrt{2}-4$$

Subtract 4 from 3 to get -1.

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