Can someone help me...it's driving me crazy!!!?

Question

I have been working on this math problem for over half an hour, even looking it up in my textbook and internet, but I just can't seem to understand this.

Here's the killer:

"Suppose you randomly selected an integer from one to a million, inclusive, and the number turned out to be a perfect square. What is the probability that the number is also a perfect cube?"

I think that the probably that it turned out to be a perfect square would be a .1% chance which is 1,000/1,000,000 chance. How do I figure out the probability that it is a perfect cube? Most understandable explanation will receive Best Answer!

Answer 1

i have this same question and i don't get it. what i was told was to look up all of the squared and cubed numbers 1-1000000. then go over it and find all the same ones. then you take that number and put it over 1000000. but i'm not sure still working on it.

Answer 2

not in school sorry cant help ya goodluck and god bless

Answer 3

You have to figure out how many of the  1-1,000,000 integers are both   square numbers and cube numbers. then you have to example it! so you would take a number that was a square number and see how many go into cube numbers. you just have to figure out witch numbers  go into both square and cube numbers.

hope this helps and Good Luck!

-Brooke

Answer 4

You have to figure out how many numbers are both perfect squares and perfect cubes.

n^2 = m^3

Suppose, x = n^6 = m^6

Then, x = (n^2)^3 = (m^3)^2

So you know that for any power of 6, you have a number that is a perfect square and a perfect cube.  I doubt you need a proof that this is the case only if they share a factor(if you do message me, and i'll come up with it, I'm not sure that it's true, just going on intuition, so you should try to find a counterexample).

The next step is to find how many powers of 6 are less than 1,000,000.  We can do this by finding the 6th root of 1,000,000 which is 10.  So there are only 10 numbers less than 1,000,000 that are both perfect square and perfect cubes.

So now, you want to find how many perfect squares there are, since you are given that you can assume you picked out a perfect square.  same idea, as above, there are 1,000

So the chances are 10/1000 = 1/100, 1%

Actually, here:

Suppose, a^2=x=b^3

Every number has a unique prime factorization.

x = q1.q2.q3....qN.=a^2=b^3

This means that the factors of a^2 and b^3 are the same, and therefore the solution is, as i stated above, only possible when you have x^6=(a^2)^3=(b^2)^3

Thanks for the problem.   =D