Which of the following is equivalent to 4-root(x^2 + 8x + 16) , where x > 0 ?

The correct answer is D. Choice D is correct. The given expression can also be written as (x^2 + 8x + 16)^1/4 . The trinomial x^2 + 8x + 16 can be rewritten in factored form as (x + 4)^2 . Thus, the entire expression can be rewritten as ((x + 4)^2)^1/4 . Simplifying the exponents yields (x + 4)^1/2 .

Note: The listed positive x-values make the fourth root expression and choice D print the same outputs.