Solve -3.14^circ-1sqrt{3}-21+1/sqrt{3}-3tan30^circ-(-1/2)^-1

$$- 3.14 ^ { \circ } - 1 \sqrt { 3 } - 21 + \frac { 1 } { \sqrt { 3 } } - 3 \tan 30 ^ { \circ } - ( - \frac { 1 } { 2 } ) ^ { - 1 }$$

Evaluate

$$-\frac{5\sqrt{3}}{3}-22.14\approx -25.026751346$$

Solution Steps

Subtract 21 from -3.14 to get -24.14.

$$-24.14-\sqrt{3}+\frac{1}{\sqrt{3}}-3\tan(30)-\left(-\frac{1}{2}\right)^{-1}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$-24.14-\sqrt{3}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-3\tan(30)-\left(-\frac{1}{2}\right)^{-1}$$

The square of \sqrt{3} is 3.

$$-24.14-\sqrt{3}+\frac{\sqrt{3}}{3}-3\tan(30)-\left(-\frac{1}{2}\right)^{-1}$$

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

$$-24.14-\frac{2}{3}\sqrt{3}-3\tan(30)-\left(-\frac{1}{2}\right)^{-1}$$

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

$$-24.14-\frac{2}{3}\sqrt{3}-3\times \frac{\sqrt{3}}{3}-\left(-\frac{1}{2}\right)^{-1}$$

Cancel out 3 and 3.

$$-24.14-\frac{2}{3}\sqrt{3}-\sqrt{3}-\left(-\frac{1}{2}\right)^{-1}$$

Combine -\frac{2}{3}\sqrt{3} and -\sqrt{3} to get -\frac{5}{3}\sqrt{3}.

$$-24.14-\frac{5}{3}\sqrt{3}-\left(-\frac{1}{2}\right)^{-1}$$

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

$$-24.14-\frac{5}{3}\sqrt{3}-\left(-2\right)$$

The opposite of -2 is 2.

$$-24.14-\frac{5}{3}\sqrt{3}+2$$

Add -24.14 and 2 to get -22.14.

$$-22.14-\frac{5}{3}\sqrt{3}$$