Simplify square root of x^2+8x+16

Problem

the square root of x squared plus 8 x plus 16

Solution

1. Identify the expression inside the square root as a quadratic trinomial of the form a x squared plus b x plus c

2. Recognize that the radicand x squared plus 8 x plus 16 is a perfect square trinomial because it follows the pattern a squared plus 2 a b plus b squared where a equals x and b equals 4

3. Factor the quadratic expression into its squared binomial form.

x squared plus 8 x plus 16 equals open paren x plus 4 close paren squared

4. Apply the property of square roots the square root of u squared equals the absolute value of u to simplify the expression.

the square root of open paren x plus 4 close paren squared equals the absolute value of x plus 4

Final Answer

the square root of x squared plus 8 x plus 16 equals the absolute value of x plus 4

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