Because the square root of 5 is an infinite acyclic decimal (that is, irrational number), it can only be written as √5. The arithmetic square root is that the square of a number is equal to the number itself, and the root is the number itself.
The history of the concept of arithmetic square root can be traced back to ancient times. Around 2000 BC, the Babylonians began to explore the problem of solving equations, including finding the square root. The ancient square root is not what we call arithmetic square root now, but the square root based on geometric intuition. It was not until the 7th century AD that the Indian mathematician Brahma gave the definition and solution of arithmetic square root correctly for the first time. Soon after, the Persian mathematician Arabs developed a method to calculate the arithmetic square root and introduced it to Europe. Since then, the concept of arithmetic square root has gradually become a basic concept in modern mathematics.