Finding cube root on a scientific calculator

[mklotz]

Every scientific calculator has a square root key but there are never cube root keys. So how does one compute a cube root on such a calculator?

You may have noticed that there is a key labeled "LOG". That key is used to find the base 10 common logarithm of a number and it is the (excuse the pun) key to finding cube, and other, roots.

You may have forgotten the definition of a logarithm. The logarithm of a number N, call it "p", is the number such that, if 10 is raised to the 'p' power, the result will be N. In equation form...

p = log(N)

N = 10^p = 10^[log(N)] (where the circumflex, "^", is used to indicate exponentiation)

All root problems, including square and cube, can be expressed as an equation...

X^m = N

[If m = 3, then X must be the cube root of N; X will always be the mth root of N.]

Take the log of both sides of this equation...

m * log(X) = log(N) (the asterisk is used to denote multiplication)

and solve for log(X)

log(X) = log(N) / m

Now X can be found using the definition of a logarithm mentioned above...

X = 10^[log(X0] = 10^[log(N) / m]

Using this formula, we can find any root, "m" of any number, "N".

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Clever readers may have noticed that there is a key labeled "LN" on their calculator. It calculates the so-called natural logarithm of a number and uses the irrational Euler's number, e = 2.718281828459045... as its base. The utility of this form of logarithm becomes apparent in calculus. While it can be used to calculate roots as shown above, I suggest you stick with common logs for now.