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Name: Michael M.
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Question:
How to solve cube roots? I know you can solve a cube root of x by raising x to the 1/3 power... But if you were to break this down into simpler mathematics (For example, bit and byte calculations on a computer chip) what is ACTUALLY done when you raise a number to a fractional power?



Replies:
Michael,

A computer does not ACTUALLY raise a number to a fractional power. A computer system is based on a huge set of approximations that eventually give a result close enough to the true value to satisfy the users of the machine. Most computer functions are actually an extremely long set simpler functions: adding and multiplying. The first approximation may be within 50 percent of the true value. The second approximation may be within 10 percent. Each new approximation is used to find the next one. Eventually, there is a small enough change from one to another that the value is accepted.

Taking the cube root of a number, or raising a number to the 1/3 power, actually is not all that complex. Finding the cube root of 2 is finding whatever number you can raise to the third power to yield 2. There is no exact decimal value for it. There is no exact fraction for it. A calculator or computer can only produce an approximation. Different computers can use slightly different programs to do it.


Dr. Ken Mellendorf
Illinois Central College



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