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

 

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 \(length \times length\) or \((length)^2\). You can use \(width \times width\) or \((width)^2\) if you are using the width of the square.

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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.

Integer Perfect Square
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100

 

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 \(x^{\frac{1}{2}}\).

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

Perfect Square Square Root Integer
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
100 10
121 11
144 12

 

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 \(^2\) 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.