Simplify Square Root of 59616

Here we will show you two methods that you can use to simplify the square root of 59616. In other words, we will show you how to find the square root of 59616 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.

√59616 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59616 to simplify the square root of 59616. 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 59616. The factors of 59616 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 69, 72, 81, 92, 96, 108, 138, 144, 162, 184, 207, 216, 276, 288, 324, 368, 414, 432, 552, 621, 648, 736, 828, 864, 1104, 1242, 1296, 1656, 1863, 2208, 2484, 2592, 3312, 3726, 4968, 6624, 7452, 9936, 14904, 19872, 29808, and 59616. Furthermore, the greatest perfect square on this list is 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Calculate 59616 divided by the greatest perfect square from the list of all factors of 59616. We determined above that the greatest perfect square from the list of all factors of 59616 is 1296. Furthermore, 59616 divided by 1296 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 59616 in its simplest radical form as follows:

√59616 = A√B

√59616 = 36√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59616 to simplify the square root of 59616 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 59616 and then take the square root of that product. The prime factors that multiply together to make 59616 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Divide 59616 by the number (A) squared. 36 squared is 1296 and 59616 divided by 1296 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 59616 in its simplest radical form as follows:

√59616 = A√B

√59616 = 36√46

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