To find the distance between the points \((-8, -3)\) and \((-2, -5)\), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, let \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).
Now, we can calculate the differences:
\[ x_2 - x_1 = -2 - (-8) = -2 + 8 = 6 \]
\[ y_2 - y_1 = -5 - (-3) = -5 + 3 = -2 \]
Now, plug these values into the distance formula:
\[ d = \sqrt{(6)^2 + (-2)^2} \]
Calculating \(6^2\) and \((-2)^2\):
\[ d = \sqrt{36 + 4} = \sqrt{40} \]
We can simplify \(\sqrt{40}\) as follows:
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Now, we can approximate \(\sqrt{10}\). The square root of 10 is approximately 3.1623, so:
\[ d \approx 2 \times 3.1623 \approx 6.3246 \]
Rounding to the nearest hundredth gives us:
\[ d \approx 6.32 \]
Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(\boxed{6.32}\).
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