The Square and Cube of a number

The square of a number / squaring numbers:

The square of a number is the multiplication of a number with itself. Sometimes, the procedure is referred “Squaring Numbers” as well.
 For Example:
 \( \displaystyle 6.6=6^2 \)
 Read as: The square of 6 or 6 squared

\( \displaystyle 5.5=5^2 \)
Read as: The square of 5 or 5 squared

\( \displaystyle 11.11=11^2 \)
Read as: The square of 11 or 11 squared


Above equations can be written in following forms;

 \( \displaystyle 6^2=6.6=36 \) 
\( \displaystyle 5^2=5.5=25\) 
\( \displaystyle 11^2=11.11=121 \) 

Why is this calculation called ‘squaring a number?

The term squaring is derived from the geometrical concept of the square. So that,
To square anything, means to actually turn it into a square.

To find the area of the square (i.e. how many unit squares are inside the main square), we multiply both sides with one another.
There are 5 squares at the bottom row, and there are 5 rows.

 5 units . 5 units= 25 unit²

25 unit squares... there are 25 squares within the square. Count if you like...

Note that, the statement  \( \displaystyle 5^2=5.5=25 \)  is called “five squared”.

The Cube of a Number

The cube of a number is three times multiplication of the number with itself. The result is called the cube of the (number) or (number) cubed. 

For Example: 

\( \displaystyle 7^3=7.7.7=343\)
The cube of 7 or 7 cubed

\( \displaystyle 12^3=12.12.12=1728\)
The cube of 12 or 12 cubed

\( \displaystyle 5^3=5.5.5=125\)
The cube of 5 or 5 cubed

Why do we call it the cube of a number?

In geometry, one must multiply the length of edges to find the volume of the cube. The procedure is also referred to as being “cubed”.

For example, the volume of a cube with a 3-unit side is: 3 units. 3 units. 3 units = 27 unit³

If you count, you will see there are 27 cubes inside.