Establish Rules and Patterns

To develop a knowledge of square roots, the following laws and patterns are broken down:

Perfect Squares

1. Ending Figure Pattern: If a number is a perfect square, then the digit at the unit position of that number must be 0, 1, 4, 5, 6 or 9. It is a quick tip to check whether a number can be a perfect square or not. (For example, 25 is a perfect square, because 5 so 23 would not be a perfect square, because 3 is not.)
2. Odd Numbers Subtraction in Sequence: Subtraction of odd numbers in sequence to get a perfect square. Start from 1 and keep incrementing 2, 4, 6 and so on…. This sequence represents the squares of natural numbers (1, 4, 9, 16, …).

General Square Roots

1. Non-negative Integers: A negative number doesn’t have a square root because the square of any number from the real number systems will always be zero or positive.
2. Perfect Square vs Imperfect Square: A perfect square can be written in the form of a fraction, and it has a rational square root. For almost all numbers this square root of the imperfect square is an irrational number so cannot be expressed as a reduced fraction. The examples are √2 (an irrational root, not being a perfect square) and √4 ( a perfect square, root = 2).
3. Radical Simplification: Perfect squares can occasionally be factored out from under the radical symbol (√) to simplify square roots. For instance, since 32 can be expressed as 16 x 2 (a perfect square), √32 can be reduced to 4√2.

Square roots are one of the important concepts in mathematical representations that can be used in various real-life applications that are evenly used in the inverse operation of square numbers, and can also be used for finding the size of a square’s side if you know its entire area. Therefore, Teaching square roots involves presenting the idea to the class, having them investigate its characteristics, and giving them practice and application chances.