Solve 4sin(60)-left|-2right|-sqrt{12}+-1^2016

$$4 \sin ( 60 ) - \left| -2 \right| - \sqrt{ 12 } + { -1 }^{ 2016 }$$

Evaluate

$$-1$$

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$4\times \frac{\sqrt{3}}{2}-|-2|-\sqrt{12}+\left(-1\right)^{2016}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{3}-|-2|-\sqrt{12}+\left(-1\right)^{2016}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$2\sqrt{3}-2-\sqrt{12}+\left(-1\right)^{2016}$$

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}.

$$2\sqrt{3}-2-2\sqrt{3}+\left(-1\right)^{2016}$$

Combine 2\sqrt{3} and -2\sqrt{3} to get 0.

$$-2+\left(-1\right)^{2016}$$

Calculate -1 to the power of 2016 and get 1.

$$-2+1$$

Add -2 and 1 to get -1.

$$-1$$