A right triangle has legs of length 8 and 15. What is the length of the hypotenuse?

Apply the Pythagorean theorem: $c^2 = 8^2 + 15^2 = 64 + 225 = 289$, so $c = \sqrt{289} = 17$, choice B. This is the well-known 8-15-17 triple. Choice A (23) adds the legs instead of using the theorem. Choice C (13) is the hypotenuse of a 5-12-13 triangle, a different triple. Choice D (161) is $15^2 - 8^2 = 225 - 64$, the difference of the squares, which would be right only if you were solving for a leg and had the hypotenuse. The hypotenuse is the sum of the squares under the root.