radical operation sqrt(x^2+9)

Question

why does this have no solution
sqrt(x^2+9)
can't i just say that the solution is x+3

Answer 1

The solution is not x + 3.  Just test it.  Is (x + 3)² = x² + 9 ?

 

(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9 ≠ x² + 9

 

x² + 9 cannot be factored or simplified further, so you cannot further simplify √(x² + 9).

 

Note:  Do not assume that the square root of a sum is the sum of the square roots.  That is not generally true.