How Do Square Numbers and Square Roots Work?

While working through math problems, you may come across the term “square,” such as 6² (six-squared) or the square root of 16. In this case, we’re not talking about shapes. If you’re wondering how square numbers and square roots work, here are some things that you should know.

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Square Numbers

You’ll know that you need to square a number when you see a 2 in superscript. For example,

When dealing with square numbers, you may hear terms like “squared” or “exponents.” Squaring any number simply involves multiplying that number by itself. In this example, we can discover the answer by writing the problem out:

It should be noted that the answer will be a non-negative, even when you start with a negative number. For example:

But what happens when the base number is 0? Since 0 x 0 = 0, then:

Square Roots

Square roots involve the inverse operation of squaring. Therefore, you need to determine what number you need to multiply by itself to come up with the number under the radical. You’ll know that you need to find the square root when you see the radical, such as:

Sometimes, you’ll end up with perfect squares. These are numbers with a square root that is a whole number. However, most of the time you’ll end up with decimal numbers. Some of the numbers that are perfect squares include:

Finding Square Roots: Prime Factorization

One way to discover the square root of a number is to use prime factorization. This is done by breaking down larger numbers into smaller perfect roots, if possible. For example:

As you work to discover the perfect squares to use, try dividing the number by smaller numbers, such as 2 or 3. Continue to divide the number until you can pull out several perfect square roots.

If the number doesn’t factor perfectly, you should just reduce the solution to the simplest form. One example of this is:

Since the square root of 3 would involve decimal numbers (1.73205080757), you can leave the number under the radical. Your final solution would be:

Finding Square Roots: Calculators

If you have a scientific calculator, you can quickly find the square root of any number. To do this, first find the radical key. After pushing this key, add the number for which you would like to find the square root. Since the number may include several places after the decimal, plan on rounding the number to the nearest hundredth or thousandth.

Knowing how to find squares and square roots is important, especially when learning about normal distributions. Choose to calculate the square root by hand or using a calculator based on how precise you want the answer.