What are Square Roots?
Definition of a square root: The opposite of squaring a number. For example, finding the square root of 81 is the same as asking, "what number, when squared, is equal to 81?"
Of course, if you know that 9 x 9 = 81, you will know that the square root of 81 is 9 (92 = 81). However, what you might not realize is that -9 is also a square root of 81, because -9 x -9 also equals 81.
In other words, all numbers greater than zero (zero can never be negative or positive) have two square roots -- one positive and one negative. This is why when using an online square root calculator, the result will always be preceded by a ± sign.
As for negative numbers, since a negative times a negative always yields a positive number, negative numbers cannot have a real value square root.
What Are Perfect Squares?
When a number has a square root that is a whole number, that number is said to be a perfect square. For example, since √4 has a square root of 2, 4 is said to be a perfect square. Here is a list of the perfect squares up to 225:
| √1 | = | 1 | since | 12 | = | 1 |
| √4 | = | 2 | since | 22 | = | 4 |
| √9 | = | 3 | since | 32 | = | 9 |
| √16 | = | 4 | since | 42 | = | 16 |
| √25 | = | 5 | since | 52 | = | 25 |
| √36 | = | 6 | since | 62 | = | 36 |
| √49 | = | 7 | since | 72 | = | 49 |
| √64 | = | 8 | since | 82 | = | 64 |
| √81 | = | 9 | since | 92 | = | 81 |
| √100 | = | 10 | since | 102 | = | 100 |
| √121 | = | 11 | since | 112 | = | 121 |
| √144 | = | 12 | since | 122 | = | 144 |
| √169 | = | 13 | since | 132 | = | 169 |
| √196 | = | 14 | since | 142 | = | 196 |
| √225 | = | 15 | since | 152 | = | 225 |
If you are still having a hard time understanding square roots, please let me know in the feedback form located beneath the calculator, and I will try to improve my explanations on this page.
Can I get a "root! root!"? :-)