Find the distance between the points. Give an exact answer and an approximation to three decimal places. \( (-6,-5) \) and \( (-16,-1) \) The exact distance is \( \square \) . (Simplify your answer. Type an exact answer, using radicals as needed.) The approximate distance is \( \square \) . (Round to the nearest thousandth as needed.)

**Step 1: Determine the coordinates.** The points given are \( (-6,-5) \) and \( (-16,-1) \). **Step 2: Compute the differences of the coordinates.** Let the first point be \( (x_1, y_1) = (-6, -5) \) and the second point be \( (x_2, y_2) = (-16, -1) \). The differences are: \[ \Delta x = x_2 - x_1 = -16 - (-6) = -10 \] \[ \Delta y = y_2 - y_1 = -1 - (-5) = 4 \] **Step 3: Use the distance formula.** The distance \( d \) between the two points is given by: \[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(-10)^2 + (4)^2} = \sqrt{100 + 16} = \sqrt{116} \] **Step 4: Simplify the square root.** Notice that \( 116 = 4 \times 29 \), so: \[ \sqrt{116} = \sqrt{4 \times 29} = \sqrt{4}\sqrt{29} = 2\sqrt{29} \] Thus, the exact distance is: \[ \boxed{2\sqrt{29}} \] **Step 5: Find the approximate value.** First, estimate \( \sqrt{29} \): \[ \sqrt{29} \approx 5.385 \] Then, multiply by 2: \[ 2\sqrt{29} \approx 2 \times 5.385 = 10.770 \] Thus, the approximate distance to three decimal places is: \[ \boxed{10.770} \]