To simplify the given expression $\sqrt{x^2+4x+4}$, we should first try to simplify the expression inside the square root.

1. Start by factoring the quadratic expression inside the square root: $x^2 + 4x + 4$ Notice that this quadratic expression can be factored as: $x^2 + 4x + 4 = (x + 2)^2$

2. Substitute the factored form back into the square root: $\sqrt{x^2 + 4x + 4} = \sqrt{(x + 2)^2}$

3. Since the square root and the square are inverse operations, they cancel each other out. However, we must consider the absolute value to account for both positive and negative values: $\sqrt{(x + 2)^2} = |x + 2|$

Therefore, the simplified form of $\sqrt{x^2 + 4x + 4}$ is $|x + 2|$.

Would you like any more details or have any questions about this process?

Here are some more questions you might find interesting:

1. How do you simplify $\sqrt{x^2 + 6x + 9}$?
2. Can you explain the properties of square roots and absolute values?
3. What are the steps to solve a quadratic equation by factoring?
4. How do you determine the vertex form of a quadratic equation?
5. What is the difference between solving an equation and simplifying an expression?

Tip: When simplifying square roots of quadratic expressions, always look to factor the quadratic expression first.