1. The problem is to simplify the expression $\sqrt{3} - (-0.0027)^{\frac{1}{3}}$. 2. Recall that $\sqrt{3}$ means the square root of 3, which is $3^{\frac{1}{2}}$. 3. The term $(-0.0027)^{\frac{1}{3}}$ means the cube root of $-0.0027$. 4. Calculate $\sqrt{3}$: $$\sqrt{3} = 3^{\frac{1}{2}} \approx 1.732$$ 5. Calculate the cube root of $-0.0027$: $$(-0.0027)^{\frac{1}{3}} = - (0.0027)^{\frac{1}{3}}$$ 6. Since $0.0027 = 27 \times 10^{-4}$, and $27^{\frac{1}{3}} = 3$, we have: $$ (0.0027)^{\frac{1}{3}} = (27 \times 10^{-4})^{\frac{1}{3}} = 3 \times 10^{-\frac{4}{3}} $$ 7. Calculate $10^{-\frac{4}{3}} = 10^{-1.3333} \approx 0.0464$. 8. So, $$ (0.0027)^{\frac{1}{3}} \approx 3 \times 0.0464 = 0.1392 $$ 9. Therefore, $$ (-0.0027)^{\frac{1}{3}} \approx -0.1392 $$ 10. Substitute back into the original expression: $$ \sqrt{3} - (-0.0027)^{\frac{1}{3}} \approx 1.732 - (-0.1392) = 1.732 + 0.1392 = 1.8712 $$ Final answer: $$1.8712$$