Square and Square Root

Square and Square Root

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: 32, 42, x2

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.

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