Square Roots Calculator

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Working with square roots is an exciting topic for math students, but they can be tricky. Beginner mathletes often rely on assumptions, like mistaking the square of 3 to be 6 just because 6 feels like 3 counted twice. But squaring involves multiplication, not addition. When we square 3 (or multiply 3 by itself), we get 9—the square root of 9 is 3.  

Square roots don't have to be a tough subject, though. In fact, it's easy to memorize the table of perfect squares and impress your teacher. But working with imperfect squares—or those numbers whose square roots contain fractions or decimals—may not always be quite that simple. This is where our free online Square Root Calculator comes in. 

How to Use Our Free Online Square Root Calculator

As with several of our other calculators, this free online square root calculator is extremely easy to use. There are only four parts of the calculator:

  • Number field
  • Calculate button
  • Clear button
  • Square Root field

To find the square root using our free online Square Root Calculator:  

  1. Click CLEAR to refresh the calculator.
  2. Enter the value whose square root you want to find into the number field.
  3. Click CALCULATE.
  4. Your answer will appear in the square root field.
  5. Click CLEAR to start over and find another value.
Number: 
Square Root:     


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What is a Square Root?

Square root refers to any number that gives you the original number as the product when multiplied by itself. Expressed with the symbol "√, "square roots belong to the family of exponents. Squares and roots are special exponents. Any square x is simply x raised to the power of ½, or x1/2.

Example

For example, when asked for the square root of 16, you look for the number that will give you a product of 16 when multiplied by itself. That number is 4 because 4 multiplied by 4—or raised to the power of 2 (mathematically expressed as 42)—is 16. 161/2 is 4.

Working with Perfect Squares

Perfect squares are positive numbers whose square roots are whole numbers. Below are the most common ways to find the square roots of these perfect squares.

Repeated Subtraction

Subtract consecutive odd numbers (1, 3, 5, 7, etc.) starting with 1, from the number whose square root you are trying to find until you arrive at 0. 

For example: 

  1. 9 - 1 = 8
  2. 8 - 3 = 5
  3. 5 - 5 = 0

You performed 3 subtractions to 0. The square root of 9 is 3.

Prime Factorization

There are four steps involved in this method. Let's go through each one to find the square root of 144. 

  1. Break down 144 into its prime factors.
    • 2, 2, 2, 2, 3, and 3.
  2. Pair up similar factors. 
    • (2x2) x (2x2) x (3x3)  
  3. Multiply one factor from each pair.
    • 2 x 2 x 3 = 12
  4. The square root of 144 is 12.

Imperfect Squares: Estimation and Long Division

Repeated subtraction and prime factorization work really well for perfect squares and occasionally for imperfect squares. For imperfect squares, you can also use estimation and long division. 

Estimation is a long process. To find the square root through estimation, you'll need to back it up with actual calculations. In long division, you divide big numbers into smaller steps to make the process easier. 

But if you get stuck, you always have our free online Square Root Calculator to help you out!

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