When two dice are thrown what is the probability of getting a product which is a perfect square?

the perfect squares are: 1*1 = 1 2*2 = 4 3*3 = 9 4*4 = 16 5*5 = 25 6*6 = 36 the number of possible products when you throw 2 dice is equal to 6 * 6 = 36 they are: 1*1 = 1 *** 1*2 = 2 1*3 = 3 1*4 = 4 *** 1*5 = 5 1*6 = 6 2*1 = 2 2*2 = 4 *** 2*3 = 6 2*4 = 8 2*5 = 10 2*6 = 12 3*1 = 3 3*2 = 6 3*3 = 9 *** 3*4 = 12 3*5 = 15 3*6 = 18 4*1 = 4 *** 4*2 = 8 4*3 = 12 4*4 = 16 *** 4*5 = 20 4*6 = 24 5*1 = 5 5*2 = 10 5*3 = 15 5*4 = 20 5*5 = 25 *** 5*6 = 30 6*1 = 6 6*2 = 12 6*3 = 18 6*4 = 24 6*5 = 30 6*6 = 36 *** out of these only 8 generate a perfect square. the probbility of getting a perfect square is therefore 8/36 = 4/18 = 2/9. note that there are more possible factors of two number that equal a perfect square, but the highest factor has to be less than or equal to 6 which is the maximum number possible on one 6 sided die. for example: 16 = 1*16 or 2*8 ot 4*4 or 8*2 or 16*1 out of all these factors, only 1 is possible, which is 4*4. the only one where all possible factors can be considered is 4. 4 is the product of 1*4 or 2*2 or 4*1. all these factors are possible when you are throwing 2 die.

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