Solve 4cos30^circ+1-sqrt{12}div|-2|

$$4 \cos 30 ^ { \circ } + 1 - \sqrt { 12 } \div | - 2 |$$

Evaluate

$$\sqrt{3}+1\approx 2.732050808$$

Solution Steps

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

$$4\times \frac{\sqrt{3}}{2}+1-\frac{\sqrt{12}}{|-2|}$$

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

$$2\sqrt{3}+1-\frac{\sqrt{12}}{|-2|}$$

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}.

$$2\sqrt{3}+1-\frac{2\sqrt{3}}{|-2|}$$

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.

$$2\sqrt{3}+1-\frac{2\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$2\sqrt{3}+1-\sqrt{3}$$

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

$$\sqrt{3}+1$$