Simplify Square Root of 60264

Here we will show you two methods that you can use to simplify the square root of 60264. In other words, we will show you how to find the square root of 60264 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.

√60264 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60264 to simplify the square root of 60264. 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 60264. The factors of 60264 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 31, 36, 54, 62, 72, 81, 93, 108, 124, 162, 186, 216, 243, 248, 279, 324, 372, 486, 558, 648, 744, 837, 972, 1116, 1674, 1944, 2232, 2511, 3348, 5022, 6696, 7533, 10044, 15066, 20088, 30132, and 60264. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 60264 divided by the greatest perfect square from the list of all factors of 60264. We determined above that the greatest perfect square from the list of all factors of 60264 is 324. Furthermore, 60264 divided by 324 is 186, therefore B equals 186.

Now we have A and B and can get our answer to 60264 in its simplest radical form as follows:

√60264 = A√B

√60264 = 18√186

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60264 to simplify the square root of 60264 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 60264 and then take the square root of that product. The prime factors that multiply together to make 60264 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 31. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 60264 by the number (A) squared. 18 squared is 324 and 60264 divided by 324 is 186. Therefore, B equals 186.

Once again we have A and B and can get our answer to 60264 in its simplest radical form as follows:

√60264 = A√B

√60264 = 18√186

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