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Let's say I have the following formula:

$$\sqrt{a^2-2ab+b^2}=\sqrt{(a-b)^2}=\sqrt{(b-a)^2}$$

When do I know which one of the following I should use?:

$$\sqrt{(a-b)^2}=a-b\qquad\text{ or }\qquad \sqrt{(b-a)^2}=b-a$$

  • 6
    Square roots are non-negative by definition, so you use whichever one is non-negative. Equivalently, you use $|a - b|$.2011-06-12
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    Related: http://math.stackexchange.com/questions/41878/reason-why-the-even-root-of-a-number-always-positive/2011-06-12
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    @Qiaochu: Shouldn't this be an answer? Seeing as it is the correct answer...2011-06-12
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    I think "quadratic function" may be better than "binomial function".2011-12-15

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