Square Numbers & Square Roots

Hello. This page will be about square numbers such as 1, 4, 9 and so on.


Table Of Contents


The Area Of A Square

A square has 4 sides with equal length in each of the 4 sides. Also the square has 4 corners and at each corner two adjacent lines form a 90 degree angle.

The area of a square is the length multiplied by the width of a square. Since the length of a square is equal to the width of the square, we use (length)^2 or (width)^2.

Source: http://www.clker.com/cliparts/b/e/c/3/131406375432193858green%20square-md.png


Perfect Square Numbers

A square number is the product of a positive whole number multiplied by itself. One example of a square number is 64 as 8 \times 8 = 8^2 = 64. Other examples of perfect square numbers include 1, 4, 9, 16, 25, 36, and 49.

Here is a sample table of square numbers.

    \[\begin{array}{|c|c|} \hline \text{Integer ($x$)} & \text{Square Of The Integer ($x^{2}$)} \ \hline \hline 1 & 1 \ \hline 2 & 4 \ \hline 3 & 9\ \hline 4 & 16 \ \hline 5 & 25\ \hline 6 & 36 \ \hline 7 & 49 \ \hline 8 & 64 \ \hline 9 & 81 \ \hline 10 & 100 \ \hline \end{array}\]


Square Roots

To obtain a perfect square we multiply a positive whole number by itself. If we want to go from a perfect square and obtain that original whole number, the square root will be needed.

The square root works on non-negative numbers and is expressed as \sqrt{x}. Sometimes \sqrt{x} is expressed as x^{1/2}.

The sample table of square numbers with its square roots is shown below.

    \[\begin{array}{|c|c|} \hline \text{Perfect Square ($x$)} & \text{Square Root ($\sqrt{x}$)}\ \hline \hline 1 & 1 \ \hline 4 & 2 \ \hline 9 & 3\ \hline 16 & 4 \ \hline 25 & 5\ \hline 36 & 6 \ \hline 49 & 7 \ \hline 64 & 8 \ \hline 81 & 9 \ \hline 100 & 10 \ \hline \end{array}\]


Examples

Here are a few more examples of squares and square roots.

The square of x is x^2, the square of x^2 is x^4. In general the square of x^{a} where the exponent a is a real number is x^{2a}.

The square root of x^2 is x and the square root of x^4 is x^2. In general, the square root of x^{a} is x^{a/2} where a is a real number.

Other perfect squares with their square roots which you may encounter from time to time include:

    \[\begin{array}{|c|c|} \hline \text{Integer ($x$)} & \text{Square Of The Integer ($x^{2}$)} \ \hline \hline 11 & 121 \ \hline 12 & 144\ \hline 13 & 169\ \hline 14 & 196\ \hline 15 & 225\ \hline \end{array}\]

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