Simplify Square Root of 58560

Here we will show you two methods that you can use to simplify the square root of 58560. In other words, we will show you how to find the square root of 58560 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.

√58560 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58560 to simplify the square root of 58560. 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 58560. The factors of 58560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 61, 64, 80, 96, 120, 122, 160, 183, 192, 240, 244, 305, 320, 366, 480, 488, 610, 732, 915, 960, 976, 1220, 1464, 1830, 1952, 2440, 2928, 3660, 3904, 4880, 5856, 7320, 9760, 11712, 14640, 19520, 29280, and 58560. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 58560 divided by the greatest perfect square from the list of all factors of 58560. We determined above that the greatest perfect square from the list of all factors of 58560 is 64. Furthermore, 58560 divided by 64 is 915, therefore B equals 915.

Now we have A and B and can get our answer to 58560 in its simplest radical form as follows:

√58560 = A√B

√58560 = 8√915

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58560 to simplify the square root of 58560 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 58560 and then take the square root of that product. The prime factors that multiply together to make 58560 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 61. 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 58560 by the number (A) squared. 8 squared is 64 and 58560 divided by 64 is 915. Therefore, B equals 915.

Once again we have A and B and can get our answer to 58560 in its simplest radical form as follows:

√58560 = A√B

√58560 = 8√915

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