Simplify Square Root of 10530

Here we will show you two methods that you can use to simplify the square root of 10530. In other words, we will show you how to find the square root of 10530 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.

√10530 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10530 to simplify the square root of 10530. 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 10530. The factors of 10530 are 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 270, 351, 390, 405, 585, 702, 810, 1053, 1170, 1755, 2106, 3510, 5265, and 10530. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 10530 divided by the greatest perfect square from the list of all factors of 10530. We determined above that the greatest perfect square from the list of all factors of 10530 is 81. Furthermore, 10530 divided by 81 is 130, therefore B equals 130.

Now we have A and B and can get our answer to 10530 in its simplest radical form as follows:

√10530 = A√B

√10530 = 9√130

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10530 to simplify the square root of 10530 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 10530 and then take the square root of that product. The prime factors that multiply together to make 10530 are 2 x 3 x 3 x 3 x 3 x 5 x 13. 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 10530 by the number (A) squared. 9 squared is 81 and 10530 divided by 81 is 130. Therefore, B equals 130.

Once again we have A and B and can get our answer to 10530 in its simplest radical form as follows:

√10530 = A√B

√10530 = 9√130

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

Simplify Square Root of 10531
Here is the next square root on our list that we have simplifed for you.