Simplify square root of a^2+2ab+b^2

Problem

√(,a^2+2*a*b+b^2)

Solution

1. Identify the expression inside the square root as a perfect square trinomial.

2. Factor the trinomial using the identity x^2+2*x*y+y^2=(x+y)^2

3. Substitute the factored form back into the square root: √(,(a+b)^2)

4. Simplify the square root of a squared expression by using the absolute value property √(,x^2)=|x|

Final Answer

√(,a^2+2*a*b+b^2)=|a+b|

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