Answer:
the simplified expression for √(x^2 - 8x + 16) when x < 4 is | x - 4 |.
Explanation:
Given the expression √(x^2 - 8x + 16), we notice that the expression under the square root is a quadratic. Let's try to factor it:
x^2 - 8x + 16
This quadratic can be factored as a perfect square trinomial:
(x - 4)^2
Now we have the expression:
√((x - 4)^2)
When simplifying the square root of a square, we need to consider the domain of the variable. Since x < 4, the expression (x - 4) will always be negative or equal to zero. Therefore, when we simplify the square root, we should take the absolute value of (x - 4) to ensure that the result is non-negative:
| x - 4 |