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September 11th, 2019, 06:37 AM  #1 
Newbie Joined: Sep 2019 From: Sri Lanka Posts: 1 Thanks: 0  What is this theory called?
$\displaystyle \sqrt{4}=2$ I was said that above equation is false. And also, $\displaystyle \sqrt{a^2}=\lefta\right$ $\displaystyle \mathrm{For}\:a\ge \:0\:\mathrm{rewrite\:}\:\sqrt{a^2}=\lefta\right \:\mathrm{\:as}\:\sqrt{a^2}=a$ $\displaystyle \mathrm{For}\:a<0\:\mathrm{rewrite\:}\:\sqrt{a^2}= \lefta\right\:\mathrm{\:as}\:\sqrt{a^2}=a$ What is this theory and where can I found more about this theory? Tnx. 
September 12th, 2019, 11:38 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 220 Thanks: 94 
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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