Final answer:
The given expression 3√(32x³y³) + √(50x³y³) simplifies to 16xy by taking the cube root of each term and combining like terms.
Step-by-step explanation:
To simplify the expression 3√(32x³y³) + √(50x³y³), we first need to simplify each square root separately. The cube root of 32x³y³ can be simplified by taking the cube root of each factor: √(32) and √(x³) and √(y³), which gives us √(2³)√(x³)√(y³) = 2xy. Similarly, for the second term √(50x³y³), we simplify √(50) and the cube roots to get √(2³ * 5³)√(x³)√(y³) = 5³2xy. Now we multiply these root values by the coefficients outside the radical and add the like terms.
3³2xy + 5³2xy = 6xy + 10xy = 16xy.
Therefore, the simplified expression is 16xy.