SOLUTION: the probability of getting the product a perfect (square of a natural numbers) when two dice are thrown together,is

Question 991297: the probability of getting the product a perfect (square of a natural numbers) when two dice are thrown together,is
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
The probability of getting the product a perfect square (square of a natural number),... (answered by jim_thompson5910)

When a pair of dice are thrown, find the probability of getting two numbers whose sum is... (answered by stanbon)

WHAT IS THE PROBABILITY OF GETTING AT LEAST A SUM OF 9 WHEN TWO DICE... (answered by josmiceli)

Two unbiased dice are thrown in the air. Find the probability that the sum of the scores... (answered by AnlytcPhil)

Three dice are thrown simultaneously the probability of getting a sum six or less... (answered by Fombitz,math_helper)

Two unbiased dice are thrown in the air. Find the probability that the sum of the scores... (answered by AnlytcPhil)

When 3 dice are thrown, the probability of getting a sum of 3 is A. 1/6 B. 1/216 (answered by greenestamps,jim_thompson5910)

When 3 dice are thrown, the probability of getting a sum of 3 is A. 1/6 B. 1/216 (answered by ikleyn)

Two dices are thrown at a time. What is the probability that the sum of the numbers on... (answered by oscargut,ewatrrr)