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

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

Evaluate

$$6$$

Solution Steps

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

$$1+|-3|-\sqrt{4}+\left(\frac{1}{2}\right)^{-2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$1+3-\sqrt{4}+\left(\frac{1}{2}\right)^{-2}$$

Add 1 and 3 to get 4.

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

Calculate the square root of 4 and get 2.

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

Subtract 2 from 4 to get 2.

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

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

$$2+4$$

Add 2 and 4 to get 6.

$$6$$

Factor

$$2\times 3$$