Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?
Answer Choices
A. \dfrac{1}{10}
B. \dfrac{1}{6}
C. \dfrac{11}{60}
D. \dfrac{1}{5}
E. \dfrac{7}{30}