November 11, 2008
The cube root of negative 27 equals ...
One day when I was taking an electronics class at American River College the teacher introduced the idea of logarithms and stated that this is how calculators do powers. I then piped in that "that's why a calculator cannot do the cube root of negative 27... "

Before I could finish my thought the teacher interrupted and said "that's undefined!" When I objected that it wasn't he said "it was yesterday!" at which the whole class erupted into laughter. He then said "Besides, show me the cube root key on your calculator... "

Of course, the teacher and most of my classmates were wrong, and the teacher was wrong about two things!

If you think about it, -3*-3=9 and 9*-3=-27 therefor -3 cubed = -27 So the cube root of -27 is -3! Since any negative number sqaured is positive you can't have a square root of a negative number, and the same would go for any even root of a negative number. However, since a positive times a negative is negative, you can take the cube root or any other odd root of a negative number.

The other issue here is that the TI30 , the scientific calculator then used by 75% of his students, can do any root through INV Yx, thus to take the cube root of 27 you would type "27 INV yx 3 =" and you would get the answer "3". If you typed "-27 INV yx 3 =" you would get an error even though the answer is "-3" because it tries to take the logarithm of -27. Try this on your windows scientific calculator (view scientific) and see what it says!

You'd think that several of my 48 classmates would have realized this but many of them mocked me and not one came to my defense.

That wasn't the last time that I was right while that teacher and the entire class were wrong, but that's a story for another day.

standard windows calculator scientific configuration

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