Final answer:
To simplify √(98x^5y^3) / √(2xy), divide the coefficients and subtract the exponents of like bases under the square root to get 7x^2y√(2), which is option c.
Step-by-step explanation:
To simplify the expression √(98x^5y^3) / √(2xy), we can start by recognizing that the square root of a quotient is the quotient of the square roots, so we can rewrite our expression as √(98x^5y^3) / √(2xy) = √(98/2) * √(x^5/x) * √(y^3/y). This simplifies to √(49) * √(x^4) * √(y^2), since 98 divided by 2 is 49, and when we apply the Division of Exponentials, we subtract the exponents of like bases.
Next, we can simplify the square roots. Since 49 is a perfect square, we have √(49) = 7, and we can rewrite √(x^4) and √(y^2) as x^2 and y respectively, applying the property that √(x^n) = x^(n/2).
Therefore, the simplified expression is 7x^2y√(2), which corresponds to option c.