Finding cube root on a scientific calculator

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.

x^0.333333333 works too.

Handy to know, thanks!
All my scientific calculators, Casio 1500's ($16), FX300ES ($12), even the Wal Mart Pen Gear at only $5 now have the cube root key.
But if you don't have one handy this method gives just as accurate results.

Quote:

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Originally Posted by RetiredFAE

Handy to know, thanks!
All my scientific calculators, Casio 1500's ($16), FX300ES ($12), even the Wal Mart Pen Gear at only $5 now have the cube root key.
But if you don't have one handy this method gives just as accurate results.

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I guess the manufacturers introduced the cube root key because nobody knows what a logarithm is or its use. Anyway, thanks for the heads up. Maybe a few folks learned something about logs from my writeup. (Hey, I can hope :-)

Marv, at 75 years of age, and after 31 years as a Federal Agent overlapping with 30 years in the USMC, I have come to believe that most of the kids today won't learn to look both ways before crossing the street thanks to cellphones, but those of us who long ago learned that the day you stop learning is the day you start dying appreciate this kind of information and you posting it. Thanks again for putting this together.

I still have several copies of books of logarithms, just in case the world goes away and the batteries in the calculators all die.

And at the age of 87 I use X^(1/3) ......