Simplify Square Root of 52704

Here we will show you two methods that you can use to simplify the square root of 52704. In other words, we will show you how to find the square root of 52704 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.

√52704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52704 to simplify the square root of 52704. 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 52704. The factors of 52704 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 61, 72, 96, 108, 122, 144, 183, 216, 244, 288, 366, 432, 488, 549, 732, 864, 976, 1098, 1464, 1647, 1952, 2196, 2928, 3294, 4392, 5856, 6588, 8784, 13176, 17568, 26352, and 52704. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 52704 divided by the greatest perfect square from the list of all factors of 52704. We determined above that the greatest perfect square from the list of all factors of 52704 is 144. Furthermore, 52704 divided by 144 is 366, therefore B equals 366.

Now we have A and B and can get our answer to 52704 in its simplest radical form as follows:

√52704 = A√B

√52704 = 12√366

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52704 to simplify the square root of 52704 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 52704 and then take the square root of that product. The prime factors that multiply together to make 52704 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 61. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 52704 by the number (A) squared. 12 squared is 144 and 52704 divided by 144 is 366. Therefore, B equals 366.

Once again we have A and B and can get our answer to 52704 in its simplest radical form as follows:

√52704 = A√B

√52704 = 12√366

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