Simplify Square Root of 52569

Here we will show you two methods that you can use to simplify the square root of 52569. In other words, we will show you how to find the square root of 52569 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.

√52569 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52569 to simplify the square root of 52569. 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 52569. The factors of 52569 are 1, 3, 9, 11, 27, 33, 59, 81, 99, 177, 297, 531, 649, 891, 1593, 1947, 4779, 5841, 17523, and 52569. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 52569 divided by the greatest perfect square from the list of all factors of 52569. We determined above that the greatest perfect square from the list of all factors of 52569 is 81. Furthermore, 52569 divided by 81 is 649, therefore B equals 649.

Now we have A and B and can get our answer to 52569 in its simplest radical form as follows:

√52569 = A√B

√52569 = 9√649

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52569 to simplify the square root of 52569 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 52569 and then take the square root of that product. The prime factors that multiply together to make 52569 are 3 x 3 x 3 x 3 x 11 x 59. 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 52569 by the number (A) squared. 9 squared is 81 and 52569 divided by 81 is 649. Therefore, B equals 649.

Once again we have A and B and can get our answer to 52569 in its simplest radical form as follows:

√52569 = A√B

√52569 = 9√649

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

Simplify Square Root of 52570
Here is the next square root on our list that we have simplifed for you.