When we are talking about squares here we are talking about multiplying a number by itself or "squaring" the number. One use of squaring is in finding the area of a square. If we know the length of one side of the square we can calculate the area of the square by multiplying that length by itself.
Here is a list of the squares for the numbers 1 to 12 which most people will learn when they learn their multiplication tables. It is recommended that you become familiar with this list.
![\[ \renewcommand\arraycolsep{1.5pt}\def\arraystretch{1.2} \begin{array}{ccc} \qquad &\qquad & \\ \text{Number}&\qquad &\text{Square of the number}\\ 1& & 1\\ 2& & 4\\ 3& & 9\\ 4& & 16\\ 5& & 25\\ 6& & 36\\ 7& & 49\\ 8& & 64\\ 9& & 81\\ 10& & 100\\ 11& & 121\\ 12& & 144\\ \end{array} \]](https://trachtenbergspeedmath.com/wp-content/ql-cache/quicklatex.com-3f2fa99a0e34aabcc7d6223ff8bc6d0b_l3.png "Rendered by QuickLaTeX.com")
The opposite operation to squaring is taking the square root of a number which we will look at later. Squaring is the easier operation and so it is recommended that you go through squaring before looking at square roots.
Since most people will learn the squares for the numbers 1 to 12 as part of learning their multiplication tables there is no need for a method to calculate these. In the Trachtenberg System squaring is split into two parts; the first is squaring two digit numbers and the second is squaring three digit numbers.
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