Simplify Square Root of 52224

Here we will show you two methods that you can use to simplify the square root of 52224. In other words, we will show you how to find the square root of 52224 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.

√52224 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52224 to simplify the square root of 52224. 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 52224. The factors of 52224 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 64, 68, 96, 102, 128, 136, 192, 204, 256, 272, 384, 408, 512, 544, 768, 816, 1024, 1088, 1536, 1632, 2176, 3072, 3264, 4352, 6528, 8704, 13056, 17408, 26112, and 52224. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 52224 divided by the greatest perfect square from the list of all factors of 52224. We determined above that the greatest perfect square from the list of all factors of 52224 is 1024. Furthermore, 52224 divided by 1024 is 51, therefore B equals 51.

Now we have A and B and can get our answer to 52224 in its simplest radical form as follows:

√52224 = A√B

√52224 = 32√51

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52224 to simplify the square root of 52224 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 52224 and then take the square root of that product. The prime factors that multiply together to make 52224 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Divide 52224 by the number (A) squared. 32 squared is 1024 and 52224 divided by 1024 is 51. Therefore, B equals 51.

Once again we have A and B and can get our answer to 52224 in its simplest radical form as follows:

√52224 = A√B

√52224 = 32√51

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