When n is greater than or equal to 0, it must be. By reduction to absurdity: suppose the root number n is a rational number. Let y= root number n, then y is also a rational number, both sides are squares, y 2 = n, and it is concluded that n is a complete square number, which contradicts the topic, so the root number n must be an irrational number.

Proof: Suppose √p is a rational number, let √p=a/b, where a, b and p are positive integers, and both sides are squared at the same time, so:

p=a？ /b？

Answer? =p*b？

As can be seen from the above formula, the left side is a complete square number, while the right side is B? It is also a complete square number, but p is not a complete square number, which means that the two sides of the above formula cannot be equal.

definition

In mathematics, irrational numbers are all real numbers of irrational numbers, which are numbers composed of the ratio (or fraction) of integers. When the length of two line segments is irrational, the line segments are also described as incomparable, that is, they cannot be "measured", that is, they have no length ("measured").

Common irrational numbers are: the ratio of circumference to diameter, Euler number e, golden ratio φ and so on. It can be seen that the representation of irrational numbers in the positional number system (for example, in decimal numbers or any other natural basis) will not be terminated or repeated, that is, it does not contain subsequences of numbers.