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. Factor the perfect square trinomial x2−8*x+16 by finding two numbers that multiply to 16 and add to −8

3. Rewrite the trinomial as a squared binomial: (x−4)2

4. Apply the property of square roots √(,a2)=|a| to simplify the expression.

Final Answer

√(,x2−8*x+16)=|x−4|

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