Involving Absolute Value

Why should the absolute value be included after taking the square root?

See attachment.

 

sqrt of any number has positive and negative solution
so, sqrt(x^2) is actually -x or +x
if you have |x| also means x could be -x or +x

sqrt(9/4) is same as sqrt(9)/sqrt(4)=3/2 or -3/-2 which is again=3/2

therefore, |x|=3/2

 

Are you saying that the proper way to express the answer after taking the square root is to apply an absolute value?

Sample:

x^2 = 16

sqrt{x^2} = sqrt{16}

| x | = 4

Also, | x | = 4 means that x = -4 and x = 4.

Yes?