1. ## 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?

2. ## Re: Perfect Square Probability

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 $\displaystyle \sqrt{n}$ is rational the $\displaystyle n$ is a square.

If $\displaystyle k\in\mathbb{Z}^+$ and $\displaystyle n\in[1,k^2]\cap\mathbb{Z}^+$ is random then the probability that $\displaystyle \sqrt{n}$ is rational is $\displaystyle \frac{1}{k}$.

3. ## Re: Perfect Square Probability

Basically, yes