Properties of Square Roots

Some of the important properties of the square root are as follows:

• For a perfect square number, a perfect square root exists.
• For a number ending with an even number of zeros, a square root exists.
• The square root of any negative numbers is not defined.
• For a number ending with the digits 2, 3, 7, or 8, then the perfect square root does not exist.
• For a number ending with the digits 1, 4, 5, 6, or 9, then the number will have a square root.

The square root of any numerical value is a value that on self multiplication results in the original number. ’√’ is the radical symbol used to depict the root of any number. By square root, we mean a power 1/2 of that number. For instance, let us suppose that x is the square root of any integer y, this implies that x=√y. On multiplying the eq, we also obtain x² = y. 

The square root of the square of a positive number gives the original number.

To understand the concept, we know, the square of 4 is 16, and the square root of 16, √16 = 4. Now, as we can see, 16 is a perfect square figure. This makes it easy to compute the square root of such numbers. However, to compute the square root of an imperfect square like 3, 5, 7, etc, computing root is a difficult process. 

A square root function is a one-to-one function that uses as input a positive number and returns the square root of the given input number.

f(x) = √x