## Square and Square Root

**What
is the square of a number?**

The square of a number is the number times itself. For example, the square of 3 is 3 x 3. The square of 4 is 4 x 4.

**Mathematical Sign for Square**

To show that a number is squared, a small 2 is placed to the top right of the number. Like this: 3

^{2}, 4

^{2}, x

^{2}

These signs are the same as saying "3 squared, 4 squared, and x squared."

This is also called a superscript or the power of the number. The number to the "power of 2" is the same as the number "squared" or the "square" of the number.

**Why is it called square?**

You can visualize the square of a number as an actual square. Here are some examples of squares of different numbers:

**List of Integer Squares**

Here is a list of squares from 1 to 12. You may already know these if you memorized the multiplication tables. These numbers are also called perfect squares.

**Square Root**

The square root is just opposite of the square. You can think of it as the "root" of the square or the number that was used to make the square.

**Sign for Square Root**

The sign for square root looks like this:

Some examples of square roots:

**Finding the Square Root**

One way is to try the guess and check method. This is where you guess the square root, check it out, and then make a better guess.

**Example:**What is the square root of 32?

We know 5 x 5 = 25 and 6 x 6 = 36, so the square root of 32 is somewhere between 5 and 6. We'll start out by guessing 5.5.

5.5 x 5.5 = 30.25

This is pretty close. We can now change our guess slightly to 5.6.

5.6 x 5.6 = 31.36

5.7 x 5.7 = 32.49

5.65 x 5.65 = 31.9225

Depending on how accurate a number we need for an answer, 5.65 is a good estimate for the square root of 32.

**Things to Remember**

- The square is the number times itself.
- The square is the same as the power of 2.
- The square root is the opposite of the square.