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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 3x3. The square of 4 is 4x4.

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:

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 example 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 the 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

There really isn't a good way to find a square root other than using your calculator. 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.


What is the square root of 32?

We know 5x5 = 25 and 6x6 = 36, so the square root of 30 is somewhere between 5 and 6. We'll start out by guessing 5.5.

5.5 x 5.5 = 30.25

That's 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

Kids Math Subjects

Intro to Multiplication
Long Multiplication
Multiplication Tips and Tricks
Square and Square Root

Intro to Division
Long Division
Division Tips and Tricks

Intro to Fractions
Equivalent Fractions
Simplifying and Reducing Fractions
Adding and Subtracting Fractions
Multiplying and Dividing Fractions

Decimals Place Value
Adding and Subtracting Decimals
Multiplying and Dividing Decimals

Basic Laws of Math
Rounding Numbers
Significant Digits and Figures
Prime Numbers
Roman Numerals
Binary Numbers
Mean, Median, Mode, and Range
Picture Graphs

Linear Equations - Introduction
Linear Equations - Slope Forms
Order of Operations
Ratios, Fractions, and Percentages
Solving Algebra Equations with Addition and Subtraction
Solving Algebra Equations with Multiplication and Division

Pythagorean Theorem
Surface Area
Volume of a Box or Cube
Volume and Surface Area of a Sphere
Volume and Surface Area of a Cylinder
Volume and Surface Area of a Cone

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