Simplify Square Root of 28296

Here we will show you two methods that you can use to simplify the square root of 28296. In other words, we will show you how to find the square root of 28296 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.

√28296 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 28296 to simplify the square root of 28296. 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 28296. The factors of 28296 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 131, 216, 262, 393, 524, 786, 1048, 1179, 1572, 2358, 3144, 3537, 4716, 7074, 9432, 14148, and 28296. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 28296 divided by the greatest perfect square from the list of all factors of 28296. We determined above that the greatest perfect square from the list of all factors of 28296 is 36. Furthermore, 28296 divided by 36 is 786, therefore B equals 786.

Now we have A and B and can get our answer to 28296 in its simplest radical form as follows:

√28296 = A√B

√28296 = 6√786

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 28296 to simplify the square root of 28296 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 28296 and then take the square root of that product. The prime factors that multiply together to make 28296 are 2 x 2 x 2 x 3 x 3 x 3 x 131. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 28296 by the number (A) squared. 6 squared is 36 and 28296 divided by 36 is 786. Therefore, B equals 786.

Once again we have A and B and can get our answer to 28296 in its simplest radical form as follows:

√28296 = A√B

√28296 = 6√786

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