Simplify Square Root of 55809

Here we will show you two methods that you can use to simplify the square root of 55809. In other words, we will show you how to find the square root of 55809 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√55809 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55809 to simplify the square root of 55809. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 55809. The factors of 55809 are 1, 3, 9, 13, 27, 39, 53, 81, 117, 159, 351, 477, 689, 1053, 1431, 2067, 4293, 6201, 18603, and 55809. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 55809 divided by the greatest perfect square from the list of all factors of 55809. We determined above that the greatest perfect square from the list of all factors of 55809 is 81. Furthermore, 55809 divided by 81 is 689, therefore B equals 689.

Now we have A and B and can get our answer to 55809 in its simplest radical form as follows:

√55809 = A√B

√55809 = 9√689

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55809 to simplify the square root of 55809 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 55809 and then take the square root of that product. The prime factors that multiply together to make 55809 are 3 x 3 x 3 x 3 x 13 x 53. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 55809 by the number (A) squared. 9 squared is 81 and 55809 divided by 81 is 689. Therefore, B equals 689.

Once again we have A and B and can get our answer to 55809 in its simplest radical form as follows:

√55809 = A√B

√55809 = 9√689

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 55810
Here is the next square root on our list that we have simplifed for you.