What is $(sqrt(2x+4))^2$ ?

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Answer 1 · 2015-08-09T15:45:41

$(sqrt(2x+4))^2 = 2x+4$ for all $x in RR$ or for all $x in [-2, oo)$ if you only consider $sqrt$ as a real valued function.

Note that if $x < -2$ then $2x+4 < 0$ and $sqrt(2x+4)$ has a complex (pure imaginary) value, but its square will still be $2x+4$ .

Essentially, $(sqrt(z))^2 = z$ by definition. If the square root exists, then it is a value whose square gives you back the original value.

Interestingly, $sqrt((2x+4)^2) = abs(2x+4)$ not $2x+4$

What is (sqrt(2x+4))^2(sqrt(2x+4))^2?