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

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

Evaluate

$$11$$

Solution Steps

Calculate \pi -1 to the power of 0 and get 1.

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

Add 12 and 1 to get 13.

$$13-\sqrt{3}+\frac{\sqrt{12}}{2}-\left(\frac{1}{2}\right)^{-1}$$

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}.

$$13-\sqrt{3}+\frac{2\sqrt{3}}{2}-\left(\frac{1}{2}\right)^{-1}$$

Cancel out 2 and 2.

$$13-\sqrt{3}+\sqrt{3}-\left(\frac{1}{2}\right)^{-1}$$

Combine -\sqrt{3} and \sqrt{3} to get 0.

$$13-\left(\frac{1}{2}\right)^{-1}$$

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

$$13-2$$

Subtract 2 from 13 to get 11.

$$11$$

Factor

$$11$$