Solve (1/2)^-1-sqrt[3]{-8}+sqrt{3}-21+2sin60^circ

$$( \frac { 1 } { 2 } ) ^ { - 1 } - \sqrt[ 3 ] { - 8 } + \sqrt { 3 } - 21 + 2 \sin 60 ^ { \circ }$$

Evaluate

$$2\sqrt{3}-17\approx -13.535898385$$

Solution Steps

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

$$2-\sqrt[3]{-8}+\sqrt{3}-21+2\sin(60)$$

Calculate \sqrt[3]{-8} and get -2.

$$2-\left(-2\right)+\sqrt{3}-21+2\sin(60)$$

The opposite of -2 is 2.

$$2+2+\sqrt{3}-21+2\sin(60)$$

Add 2 and 2 to get 4.

$$4+\sqrt{3}-21+2\sin(60)$$

Subtract 21 from 4 to get -17.

$$-17+\sqrt{3}+2\sin(60)$$

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

$$-17+\sqrt{3}+2\times \frac{\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$-17+\sqrt{3}+\sqrt{3}$$

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

$$-17+2\sqrt{3}$$