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