Thread: Perfect Square Probability

An integer n is randomly chosen from 1 to k^2, where k is an integer. What is the probability that n is a perfect square?

I have determined that the probability of n being a perfect square is 1/k?

If I am correct above, does this imlpy that the probability of n^(1/2) being irrational is (k-1)/k?

Originally Posted by thamathkid1729

An integer n is randomly chosen from 1 to k^2, where k is an integer. What is the probability that n is a perfect square?
I have determined that the probability of n being a perfect square is 1/k?
If I am correct above, does this imlpy that the probability of n^(1/2) being irrational is (k-1)/k?

It is well known that if the is rational the is a square.

If and is random then the probability that is rational is .
Is that your question?

Basically, yes