In the previous article on square numbers, we have learnt that when an integer (negative or positive) multiplies itself twice, we get a perfect square. So a perfect square has two equal integer factors (numbers multiplying to make a product).
For example, 64 is a perfect square because 8 (an integer) when squared
(8 x 8 ) is 64 and -8 (another integer) multiplies itself (-8 x -8) = 64.
With this recap on perfect squares, we can go into square roots. This is because we need to identify and use perfect squares when working with square roots. Square roots are the inverse or opposites of squaring. So just as we learnt the term exponent or powers of 2 in squaring numbers, we will learn in the inverse of squaring the term ‘root’. Finding the opposite of a square number is to ‘undo’ the square.
Shall we have a look at another example of numbers in the exponent :
4 to the 2nd power (four squared) = 4 x 4 = 16
To undo this, we find the inverse of the square 16 and this gives us the number, 4. This is called the base. The terms ‘root’ and ‘base’ can be easily understood as they are linked to a tree. Trying to find the roots of a tree will get you to the base.
So in doing root operation for square numbers, we start with the product (square number) and undo it by getting to its roots, to arrive at the base of the exponent. For example 16 square root = 4 and 4 squared = 16.
The 4 is the base and as it’s squared, it’s in the power of 2. So 2 is the exponent and 16 is the perfect square.
Finding the square roots of Perfect Squares
To calculate square roots, we need to know and use the perfect squares of all the single digits (from 0 to 9). That can be written down in a tabular form.
Example 2.
Example 4:
Finding the square roots of non-perfect squares.
With non-perfect squares, there is the need to have a good working knowledge of perfect squares.
Example 2:
Example 4:
You can try with more examples (checking with a calculator) to get a better understanding of calculating with square roots.