The numbers on a certain die are sqrt(1), sqrt(2), sqrt(3), sqrt(4), sqrt(5), and sqrt(6). The die is rolled twice, and the two results are multiplied. What is the probability that the product of the two rolls is rational?
sqrt1 sqrt2 sqrt3 sqrt4 sqrt5 sqrt6
sqrt1 ratn irr irr ratn irr irr
sqrt2 irr ratn irr irr irr irr
sqrt3 irr irr ratn irr irr irr
sqrt4 ratn irr irr ratn irr irr
sqrt5 irr irr irr irr ratn irr
sqrt6 irr irr irr irr irr ratn
I count 8 rational and 28 irrational
The probability =8 / 6^2 = 4 / 9
sqrt1 sqrt2 sqrt3 sqrt4 sqrt5 sqrt6
sqrt1 ratn irr irr ratn irr irr
sqrt2 irr ratn irr irr irr irr
sqrt3 irr irr ratn irr irr irr
sqrt4 ratn irr irr ratn irr irr
sqrt5 irr irr irr irr ratn irr
sqrt6 irr irr irr irr irr ratn
I count 8 rational and 28 irrational
The probability =8 / 6^2 = 4 / 9
