Square roots are factors of numbers that multiply by themselves to make a new number. In order to figure out the square root of a number, you have to look at the number inside the square root sign, and think to yourself, "What number times itself gives me the number in the symbol?" For example, if you're finding the square root of 25, you should think ? x ? = 25, and both of the ?s should be the same number. For example, the square root of 25 is 5, because 5 x 5 is 25. The square root sign looks like a division sign—with a tail. Like this:
Any time you see this sign, with a number inside, it means you need to take the square root of the number. Some numbers, like 25, are perfect squares, which means that the factors are even—they are not decimal numbers. Most numbers, however, are not perfect squares, which means that they are decimal numbers. Take, for example, the square root of 2. With the square root sign, it would look like this:
The square root of two can only be figured out on a calculator, by using the square root button (it will probably have the square root sign on it, or it might say sqrt, which is short for square root). You will press the square root key, and then enter in the number (for example, 2) and then press enter. You will get an answer that looks like this: 1.41421356. That means that 1.41421356 x 1.41421356 = 2. Many times, these decimals be extremely long, or repeat—which means they go on forever!
If you are given a square root problem and are not allowed to use a calculator, chances are the number is a perfect square. Some of the common perfect squares are 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), 64 (8 x 8), 81 (9 x 9) and 100 (10 x 10) so make sure that you’re familiar with your times tables!
Chances are if you are allowed to use a calculator, you’ll be working with square roots that have decimal answers, like the square root of 2 (or 3, or 5, or so on...)