Solve sqrt{27}+{left(-1/3right)}^-1+{left(-sqrt{2}right)}^0-6sin(60^circ)

$$\sqrt{ 27 } + { \left(- \frac{ 1 }{ 3 } \right) }^{ -1 } + { \left(- \sqrt{ 2 } \right) }^{ 0 } -6 \sin ( 60 ^ { \circ } )$$

Evaluate

$$-2$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\sqrt{3}+\left(-\frac{1}{3}\right)^{-1}+\left(-\sqrt{2}\right)^{0}-6\sin(60)$$

Calculate -\frac{1}{3} to the power of -1 and get -3.

$$3\sqrt{3}-3+\left(-\sqrt{2}\right)^{0}-6\sin(60)$$

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

$$3\sqrt{3}-3+\left(-\sqrt{2}\right)^{0}-6\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$3\sqrt{3}-3+\left(-\sqrt{2}\right)^{0}-3\sqrt{3}$$

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

$$-3+\left(-\sqrt{2}\right)^{0}$$

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

$$-3+1$$

Add -3 and 1 to get -2.

$$-2$$