Solve 4cos30^circ-sqrt{12}-(-1/2)^-2

$$4 \cos 30 ^ { \circ } - \sqrt { 12 } - ( - \frac { 1 } { 2 } ) ^ { - 2 }$$

Evaluate

$$-4$$

Solution Steps

Get the value of \cos(30) from trigonometric values table.

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

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

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

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}.

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

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

$$0-\left(-\frac{1}{2}\right)^{-2}$$

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

$$0-4$$

Subtract 4 from 0 to get -4.

$$-4$$