Simplify Square Root of 72504

Here we will show you two methods that you can use to simplify the square root of 72504. In other words, we will show you how to find the square root of 72504 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.

√72504 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72504 to simplify the square root of 72504. 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 72504. The factors of 72504 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 53, 57, 72, 76, 106, 114, 152, 159, 171, 212, 228, 318, 342, 424, 456, 477, 636, 684, 954, 1007, 1272, 1368, 1908, 2014, 3021, 3816, 4028, 6042, 8056, 9063, 12084, 18126, 24168, 36252, and 72504. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 72504 divided by the greatest perfect square from the list of all factors of 72504. We determined above that the greatest perfect square from the list of all factors of 72504 is 36. Furthermore, 72504 divided by 36 is 2014, therefore B equals 2014.

Now we have A and B and can get our answer to 72504 in its simplest radical form as follows:

√72504 = A√B

√72504 = 6√2014

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72504 to simplify the square root of 72504 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 72504 and then take the square root of that product. The prime factors that multiply together to make 72504 are 2 x 2 x 2 x 3 x 3 x 19 x 53. 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 72504 by the number (A) squared. 6 squared is 36 and 72504 divided by 36 is 2014. Therefore, B equals 2014.

Once again we have A and B and can get our answer to 72504 in its simplest radical form as follows:

√72504 = A√B

√72504 = 6√2014

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