Squaring Negative NumbersDate: 02/19/2002 at 10:59:10 From: Thanh Phan Subject: Squaring negative numbers Hello, I would like to know: does -9^2 = 81 or -81? Date: 02/19/2002 at 12:38:08 From: Doctor Rick Subject: Re: Squaring negative numbers Hi, Thanh. You really should be precise about what you are asking in this case, since (-9)^2 means -9 times -9, but the expression -9^2 could also be taken to mean -(9^2), that is, the negative of the square of 9, which is -81. When we're working with variables, if we see -x^2, we interpret it in the second way, as -(x^2), because squaring (or any exponentiation) takes precedence over negation (or any multiplication; -x is treated as -1*x. When you have numbers only, as in -9^2, it's not at all clear that we should treat it differently from -x^2. However, some will argue that it should, because -9 represents a single number, not an operation on a number. Thus, some will interpret -9^2 as (-9)^2, while others will read it as -(9^2). Because of the difference of opinion, I highly recommend that you put in the parentheses explicitly whenever this situation arises. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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