Subject: Geometry

Squares And Square Roots

Squares and square roots are important mathematical aspects that are used vastly in any mathematics and scientific discipline. It is used primarily to calculate distances, determining absolute values and many more. For example, in Einstein's famous equation regarding energy ( E = mc^2), for which he postulates that the total energy of a particle is proportional to the speed of light squared. Maybe most of you cannot understand that equation because it is advanced physics. But in this article, let me discuss to you the basics about squares and square roots.


When an integer is multiplied by itself we call the product the square of the number. So to square a number, we will only multiply it by itself. The product is called the square. We call this product as square because in geometry, the product represent the area of a square whose side is the number of integer that was multiplied by itself.

In the figure above, the area of the square is calculated by multiplying the length of the s by itself. In other words, the area of a square is the square of the sides. There are many terminologies in squaring a number. For example,

2 x 2 = 4

can also be read as; the square of two is four, two squared equals/is four and many more.

Shorthand Notation

The shorthand notation in squaring a number is to put the number 2 in the superscript of a number we want to square or multiply by itself. So for the example above, 2 x 2 = 4 can also be written as;

2^2 = 4

Square Roots

Now supposed you are given the area of a square. How would you find the lengths of its sides? This is where square roots come in. Square root is that number or integer we multiply by itself, or we squared, to get the area or the square. Actually, square root of a number are the two equal factors of that number. So, for the example 2x2=4 or 2^2=4, the square root of four is obviously two since two is the two equal factor of four.

Shorthand Notation

To symbolize or to get the square root of a number, a "radical sign" \sqrt() is placed before the number in question. For example, to get the square root of four, we write

\sqrt{4} = 2

Moreover, two is not the only square root of four. -2 is also a square root since multiplyng -2 by itself is also four. Thus, in general, a number has two square roots; the positive and negative square roots. Thus its always right to write it as

\sqrt{4} = \pm 2

Perfect Squares

Perfect squares are those squares whose square roots are integers. Few examples of perfect squares:

1.) 1: 1x1=1
2.) 4: 2x2=4
3.) 9: 3x3=9
4.) 16: 4x4 = 16