is the square root of a prime number always going to be irrational? just a random question.
This is true, and in fact the nth root of any rational number which doesn't have a perfect nth power in both the numerator and denominator (when written in lowest terms) is irrational. To see this (as I mentioned in another https://www.physicsforums.com/showthread.php?t=129729"), just note that when you take the nth power of a rational number, you get a rational number with the above property. So conversely, a number which doesn't have this property can't be the nth power of a rational number.BSMSMSTMSPHD said:In general, I think that the nth root of any natural number that is not itself a perfect nth power is an irrational number.