Solve -1^2000-(sqrt{3}-sqrt{2})^0+(1/2)^-1+2sin60

$$- 1 ^ { 2000 } - ( \sqrt { 3 } - \sqrt { 2 } ) ^ { 0 } + ( \frac { 1 } { 2 } ) ^ { - 1 } + 2 \sin 60$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Calculate 1 to the power of 2000 and get 1.

$$-1-\left(\sqrt{3}-\sqrt{2}\right)^{0}+\left(\frac{1}{2}\right)^{-1}+2\sin(60)$$

Calculate \sqrt{3}-\sqrt{2} to the power of 0 and get 1.

$$-1-1+\left(\frac{1}{2}\right)^{-1}+2\sin(60)$$

Subtract 1 from -1 to get -2.

$$-2+\left(\frac{1}{2}\right)^{-1}+2\sin(60)$$

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

$$-2+2+2\sin(60)$$

Add -2 and 2 to get 0.

$$2\sin(60)$$

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

$$2\times \frac{\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$\sqrt{3}$$