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

Problem

√(,x2+8*x+16)

Solution

1. Identify the expression inside the square root as a quadratic trinomial of the form a*x2+b*x+c

2. Recognize that the radicand x2+8*x+16 is a perfect square trinomial because it follows the pattern a2+2*a*b+b2 where a=x and b=4

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

x2+8*x+16=(x+4)2

4. Apply the property of square roots √(,u2)=|u| to simplify the expression.

√(,(x+4)2)=|x+4|

Final Answer

√(,x2+8*x+16)=|x+4|

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