Irrational numbers are real numbers, but square root of 9 which is 3 is not an irrational number, it is a rational number, and integer, whole number and a counting number. Square root of 2 is irrational, but so is pi. What makes a number irrational is not the radical sign but is that the decimal goes forever and never repeats so you can not write an irrational number as a fraction or ratio (see how ratio is part of rational.) Another example of an irrational number that doesn't use the radical sign is e. E is used when you are dealing with natural logarithms = approx 2.7183 but its decimal goes of forever also.