Simplify Square Root of 54528

Here we will show you two methods that you can use to simplify the square root of 54528. In other words, we will show you how to find the square root of 54528 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.

√54528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54528 to simplify the square root of 54528. 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 54528. The factors of 54528 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 128, 142, 192, 213, 256, 284, 384, 426, 568, 768, 852, 1136, 1704, 2272, 3408, 4544, 6816, 9088, 13632, 18176, 27264, and 54528. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 54528 divided by the greatest perfect square from the list of all factors of 54528. We determined above that the greatest perfect square from the list of all factors of 54528 is 256. Furthermore, 54528 divided by 256 is 213, therefore B equals 213.

Now we have A and B and can get our answer to 54528 in its simplest radical form as follows:

√54528 = A√B

√54528 = 16√213

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54528 to simplify the square root of 54528 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 54528 and then take the square root of that product. The prime factors that multiply together to make 54528 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 71. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 54528 by the number (A) squared. 16 squared is 256 and 54528 divided by 256 is 213. Therefore, B equals 213.

Once again we have A and B and can get our answer to 54528 in its simplest radical form as follows:

√54528 = A√B

√54528 = 16√213

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