Is Sqrt(x^2) Always Equal to |x|?

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The discussion centers on the mathematical expression sqrt(x^2) and its equivalence to |x|. While sqrt(x^2) yields a positive value, it represents the principal square root, which is always non-negative. The confusion arises from the fact that while x can be negative, the square root function only returns the positive root, thus aligning it with |x|. The example of plugging in -10 illustrates that sqrt(100) equals 10, reinforcing the point that sqrt(x^2) does not equal x for negative values. Ultimately, sqrt(x^2) is always equal to |x|, reflecting the nature of square roots and absolute values.
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Okay, when I enter into the calculator sqrt(x^2) it equals |x|. Since when? I thought sqrt(x^2) equals x and then when you go to sketch it, it will be a positive diagonal line through the origin whereas |x| is a reflection at the origin.
 
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A number squared is always positive. So if you plug in -10 you get sqrt(100) which is 10.
When you cancel out the square and the square root in a problem you do that because you're looking for the principle root aka the positive one.
 

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