Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?

Given:
Radius of first circle $r_1 = 8$ cm, radius of second circle $r_2 = 3$ cm, and distance between centers $d = 15$ cm.

For the length of a direct common tangent, we use the formula:

Length = $\sqrt{d^2 - (r_1 - r_2)^2}$

Substitute the values:

Length = $\sqrt{15^2 - (8 - 3)^2}$
= $\sqrt{225 - 25}$
= $\sqrt{200}$
= $10\sqrt{2}$

Final Answer: $10\sqrt{2}$ cm