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# Should we get rid of "absolute value" and replace it with "square root of square?"

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Proving_a_Negative
 Voting Style: Open Point System: 7 Point Started: 2/2/2015 Category: Miscellaneous Updated: 2 years ago Status: Post Voting Period Viewed: 668 times Debate No: 69339
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 Con Round 1: AcceptanceRound 2: Opening ArgumentRound 3: Rebuttal and Closing Statement Should we get rid of absolute value and replace it with the square root of the square? I believe not. This is something that I thought we should do as a kid, but now I realize that I'm wrong. Hopefully I can convince somebody else also. Good luck to my opponent. Report this Argument Pro COMO interesante! jajajajaReport this Argument Con Taking the square root of square of a number will indeed make any real number positive. The problem is, absolute value measures magnitude. Why does this matter? For imaginary numbers, the result you get with these 2 functions is different. Take sqrt(-1) for example. The abs(sqrt(-1))=1 but the sqrt(sqrt(-1)^2)=sqrt(-1). Sqrt(-1) doesn't equal 1. Therefore, we can't get rid of absolute value.Why did I bring up this topic? For algebra students, it would be nice to know how to undo an absolute value sign. Take this equation: abs(x)=3 How do you undo an absolute value? Well you could pretend that absolute value is the same as the square root of square. So the equation then looks like this: sqrt(x^2)=3 This is solvable using systematic algebra now. In both cases, x=3,-3 which is completely correct. Now let's say we have this equation: abs(x)=-3 Our trick before doesn't work simply because of reasons stated before. Let's try it out anyways. The equation will now look like this: sqrt(x^2)=-3 Solving the problem will give you x=sqrt(-3) and -sqrt(-3). Plug these answers back into the original equation: abs(x)=-3 and you will realize that it is incorrect. That is why we can't get rid of absolute value.Report this Argument Pro And a pear in a partridge treeReport this Argument Con Please vote pro for the lol factor. Thanks. :DReport this Argument Pro Thabk ya bby Disk o tech aReport this Argument
10 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Proving_a_Negative 2 years ago
Surrealism, would you like to debate this?
Posted by YassineB 2 years ago
- STFU, this is not a competition of most stupid answer. Square Root is positive, PERIOD. If you don't know this, you should probably redo your elementary education. DAMN!
Posted by Surrealism 2 years ago
Every definition for square root I can find is "a number that produces a specified quantity when multiplied by itself." That means square roots will always have plus or minus answers. Math doesn't change when used in an equation.
Posted by UndeniableReality 2 years ago
I'm not sure you'll get someone who's actually studied any math to debate you on this.
Posted by Proving_a_Negative 2 years ago
Surrealism, that only applies when you are solving an equation i.e. x^2=4
x= + or -2.
When you simply take the square root of a number, you get only one result i.e. sqrt(4)=2
Posted by Surrealism 2 years ago
The square root of a number can be written as positive or negative. Squaring negative two results in positive four, the square root of which is plus or minus two. The square root of the square does not remove the minus sign.
Posted by Proving_a_Negative 2 years ago
Dang, you couldn't have put it any better.
Posted by YassineB 2 years ago
- Absolute Value is just a particular case of Arguments which is a particular case of Norms. It just so happens that R is uni-demential Banach & Dense space that the Absolute Value coincides with the square root of square.
Posted by Proving_a_Negative 2 years ago
Taking the square root of a square will result in removing a negative sign for any real number. This is how they are similar to absolute value.
Posted by Surrealism 2 years ago
Well, they're two different concepts entirely.
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