Final answer:
To simplify the expression 2√(12xy²), separate the square root of a product into the product of square roots and simplify, leaving you with 4y√3x.
Step-by-step explanation:
To simplify the expression 2√(12xy²), we can simplify the square root of 12 to its simplest form. The prime factorization of 12 is 2² × 3, so we can rewrite the expression as 2√(2² × 3 × xy²). Using the property of square roots, we can separate the square root of a product into the product of square roots. This gives us 2(2√3)(√x)(√y²). The square root of y² is y, so the final simplified expression is 4y√3x.