Simplify Square Root of 10368

Here we will show you two methods that you can use to simplify the square root of 10368. In other words, we will show you how to find the square root of 10368 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.

√10368 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10368 to simplify the square root of 10368. 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 10368. The factors of 10368 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 288, 324, 384, 432, 576, 648, 864, 1152, 1296, 1728, 2592, 3456, 5184, and 10368. Furthermore, the greatest perfect square on this list is 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Calculate 10368 divided by the greatest perfect square from the list of all factors of 10368. We determined above that the greatest perfect square from the list of all factors of 10368 is 5184. Furthermore, 10368 divided by 5184 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 10368 in its simplest radical form as follows:

√10368 = A√B

√10368 = 72√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10368 to simplify the square root of 10368 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 10368 and then take the square root of that product. The prime factors that multiply together to make 10368 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Divide 10368 by the number (A) squared. 72 squared is 5184 and 10368 divided by 5184 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 10368 in its simplest radical form as follows:

√10368 = A√B

√10368 = 72√2

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