Evaluate $\dfrac{(-3.85)^2 - \sqrt{10 - 0.9 \times (-6)}}{3.11 - 4^3}$, giving your answer to 4 significant figures.

1. Evaluate the expression using order of operations and round to 4 significant figures.

$\frac{(-3.85)^2-\sqrt{10-0.9\times(-6)}}{3.11-4^3}$

Inside the square root,
$10-0.9\times(-6)=10+5.4=15.4.$

So

$$\frac{(-3.85)^2-\sqrt{15.4}}{3.11-64}= \frac{14.8225-3.924283\ldots}{-60.89}$$

$=\frac{10.898216\ldots}{-60.89}=-0.178982\ldots$

To 4 significant figures,
$-0.178982\ldots=-0.1790.$