Square root facts for kids
A square root is a special number in mathematics. When you multiply a number by itself, you get a new number. The square root is like going backward! It's the number you started with.
For example, if you multiply 2 by itself (2 × 2), you get 4. So, 2 is the square root of 4. Simple, right?
We use a special symbol for square roots: 
. So, 
means "the square root of 4."
Only numbers that are zero or bigger than zero have "real" square roots. The square root of zero is just zero.
The square root of 2 is a very famous number. It's about 1.41421. This number is also the length of the diagonal line in a square that has sides of length 1.
Contents
Imaginary Square Roots
What about square roots of negative numbers? These are not "real" numbers. They are called imaginary numbers. An imaginary number is a number whose square is negative.
For example, the number -1 has two imaginary square roots. We call them 
and 
. The number is known as the imaginary unit.
Perfect Squares
A whole number that has a whole number as its square root is called a perfect square.
Here are some perfect squares:
- 0 (because 0 × 0 = 0)
- 1 (because 1 × 1 = 1)
- 4 (because 2 × 2 = 4)
- 9 (because 3 × 3 = 9)
- 16 (because 4 × 4 = 16)
- 25 (because 5 × 5 = 25)
- 36 (because 6 × 6 = 36)
- 49 (because 7 × 7 = 49)
- 64 (because 8 × 8 = 64)
- 81 (because 9 × 9 = 81)
- 100 (because 10 × 10 = 100)
The list continues with 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225.
Square Root Table
Here is a table showing the square roots of numbers from 1 to 20. The numbers are rounded to three decimal places.
| Number | Square root of number |
|---|---|
| 1 | 1.000 |
| 2 | 1.414 |
| 3 | 1.732 |
| 4 | 2.000 |
| 5 | 2.236 |
| 6 | 2.449 |
| 7 | 2.646 |
| 8 | 2.828 |
| 9 | 3.000 |
| 10 | 3.162 |
| 11 | 3.317 |
| 12 | 3.464 |
| 13 | 3.606 |
| 14 | 3.742 |
| 15 | 3.873 |
| 16 | 4.000 |
| 17 | 4.123 |
| 18 | 4.243 |
| 19 | 4.359 |
| 20 | 4.472 |
Where Did the Square Root Symbol Come From?
No one is completely sure where the square root symbol came from. Some people think it might have come from the letter r. This is because r is the first letter of the Latin and German word radix.
Radix means "root" or "base." So, "radix quadratum" in Latin probably meant "the base of a square." Since all sides of a square are equal, the word radix might have been used to mean the side of a square.
Related Pages
Images for kids
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You can use a compass and straightedge to draw a line with the length of a square root.
See also
In Spanish: Raíz cuadrada para niños
