In many cases, factoring an expression can make it easier to evaluate as in the following...

In many cases, factoring an expression can make it easier to evaluate as in the following applications.

Space-Time relationships: Due to the work of Albert Einstein and other physicists who labored on space-time relationships, it is known that the faster an object moves the shorter it appears to become. This phenomenon is modeled by the

Lorentz transformation ,

where L0 is the length of the object at rest, L is the relative length when the object is moving at velocity v, and c is the speed of light. Factor the radicand and use the result to determine the relative length of a 12-in. ruler if it is shot past a stationary observer at 0.75 times the speed of light (v = 0.75c).