Simplify Square Root of 58320

Here we will show you two methods that you can use to simplify the square root of 58320. In other words, we will show you how to find the square root of 58320 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.

√58320 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58320 to simplify the square root of 58320. 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 58320. The factors of 58320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 243, 270, 324, 360, 405, 432, 486, 540, 648, 720, 729, 810, 972, 1080, 1215, 1296, 1458, 1620, 1944, 2160, 2430, 2916, 3240, 3645, 3888, 4860, 5832, 6480, 7290, 9720, 11664, 14580, 19440, 29160, and 58320. Furthermore, the greatest perfect square on this list is 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Calculate 58320 divided by the greatest perfect square from the list of all factors of 58320. We determined above that the greatest perfect square from the list of all factors of 58320 is 11664. Furthermore, 58320 divided by 11664 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 58320 in its simplest radical form as follows:

√58320 = A√B

√58320 = 108√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58320 to simplify the square root of 58320 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 58320 and then take the square root of that product. The prime factors that multiply together to make 58320 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Divide 58320 by the number (A) squared. 108 squared is 11664 and 58320 divided by 11664 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 58320 in its simplest radical form as follows:

√58320 = A√B

√58320 = 108√5

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