Simplify square root of 12x^2

Problem

√(,12*x2)

Solution

1. Factor the radicand into its prime factors and perfect squares.

√(,2⋅3⋅x2)

2. Apply the product property of square roots, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,2)⋅√(,x2)⋅√(,3)

3. Simplify the square roots of the perfect squares. Note that √(,x2)=|x|

2⋅|x|⋅√(,3)

4. Combine the terms into a single expression.

2*|x|√(,3)

Final Answer

√(,12*x2)=2*|x|√(,3)

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