Simplify Square Root of 59520

Here we will show you two methods that you can use to simplify the square root of 59520. In other words, we will show you how to find the square root of 59520 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.

√59520 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59520 to simplify the square root of 59520. 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 59520. The factors of 59520 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 128, 155, 160, 186, 192, 240, 248, 310, 320, 372, 384, 465, 480, 496, 620, 640, 744, 930, 960, 992, 1240, 1488, 1860, 1920, 1984, 2480, 2976, 3720, 3968, 4960, 5952, 7440, 9920, 11904, 14880, 19840, 29760, and 59520. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 59520 divided by the greatest perfect square from the list of all factors of 59520. We determined above that the greatest perfect square from the list of all factors of 59520 is 64. Furthermore, 59520 divided by 64 is 930, therefore B equals 930.

Now we have A and B and can get our answer to 59520 in its simplest radical form as follows:

√59520 = A√B

√59520 = 8√930

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59520 to simplify the square root of 59520 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 59520 and then take the square root of that product. The prime factors that multiply together to make 59520 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 59520 by the number (A) squared. 8 squared is 64 and 59520 divided by 64 is 930. Therefore, B equals 930.

Once again we have A and B and can get our answer to 59520 in its simplest radical form as follows:

√59520 = A√B

√59520 = 8√930

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