Find the Domain square root of x^2+4x+4

Problem

√(,x2+4*x+4)

Solution

1. Identify the condition for the domain of a square root function, which requires the radicand to be greater than or equal to zero.

x2+4*x+4≥0

2. Factor the quadratic expression inside the square root.

(x+2)2≥0

3. Analyze the inequality. Since any real number squared is always non-negative, the inequality holds true for all real values of x

x∈ℝ

Final Answer

Domain of √(,x2+4*x+4)=(−∞,∞)

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