Why Don't Calculators Accept (-2)^(2/3)?Date: 02/17/2002 at 06:06:18 From: Aaron Kim Subject: Index number Dear Dr. Math, (-2)^(2/3) = cubic root of (-2)^2 = cubic root of 4 = 1.587 Theoretically the above calculation is right; however, if you punch in (-2_^(2/3) in a scientific calculator, it gives an error message. That is undefined. Could you explain why? Best regards. Aaron. Date: 02/17/2002 at 08:00:47 From: Doctor Jerry Subject: Re: Index number Hi Aaron, Most calculators evaluate a^b this way: a^b = e^{ln(a^b)} = e^{b*ln(a)}. So, if a is negative, your calculator may give an error message - for the reason that the domain of the ordinary logarithm function is the set of all positive numbers. My HP48GX gives (-2)^{2/3} = -0.7937... + i*1.3747... for an answer. Your result, 1.587..., is also an answer. The fact is that there are several answers. There are three cube roots of 4. If you cube -0.7937... + i*1.3747... you will obtain 4 (except for rounding error). - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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