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  • 1 Post By DarnItJimImAnEngineer
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September 11th, 2019, 06:37 AM   #1
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What is this theory called?

$\displaystyle \sqrt{4}=-2$


I was said that above equation is false.


And also,

$\displaystyle \sqrt{a^2}=\left|a\right|$



$\displaystyle \mathrm{For}\:a\ge \:0\:\mathrm{rewrite\:}\:\sqrt{a^2}=\left|a\right| \:\mathrm{\:as}\:\sqrt{a^2}=a$


$\displaystyle \mathrm{For}\:a<0\:\mathrm{rewrite\:}\:\sqrt{a^2}= \left|a\right|\:\mathrm{\:as}\:\sqrt{a^2}=-a$

What is this theory and where can I found more about this theory?
Tnx.
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September 12th, 2019, 11:38 AM   #2
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I don't know about a theory, but every mathematical convention I have ever seen took √ to represent the principal square root, which is exactly what you have described (for positive, real numbers).
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