Is the square root of -17 a rational or irrational number? - Answers

The square root of 17 is an irrational number. The square root of any number (with the exception of perfect squares, of course) is an irrational number. A rational number is any number that can be represented as a fraction (or ratio, hence the name). So take two numbers, say p and q, whose greatest common factor is 1, and put p over q: p / q. For instance, 0.1 is a rational number, because it can be represented as 1/10. The same can be said for 0.25, 0.190329, and even integers such as 5 (written as 5/1). Irrational Numbers can't be expressed as fractions, or ratios, hence their name - it has nothing to do with the sanity of a number! As has been proven elsewhere, pi (3.14159265...) is irrational, as is Euler's number (e). And of course, as I said above, the square root of any number that is not a perfect square is an irrational number.