Simplify Square Root of 64800

Here we will show you two methods that you can use to simplify the square root of 64800. In other words, we will show you how to find the square root of 64800 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.

√64800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64800 to simplify the square root of 64800. 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 64800. The factors of 64800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 96, 100, 108, 120, 135, 144, 150, 160, 162, 180, 200, 216, 225, 240, 270, 288, 300, 324, 360, 400, 405, 432, 450, 480, 540, 600, 648, 675, 720, 800, 810, 864, 900, 1080, 1200, 1296, 1350, 1440, 1620, 1800, 2025, 2160, 2400, 2592, 2700, 3240, 3600, 4050, 4320, 5400, 6480, 7200, 8100, 10800, 12960, 16200, 21600, 32400, and 64800. Furthermore, the greatest perfect square on this list is 32400 and the square root of 32400 is 180. Therefore, A equals 180.

B = Calculate 64800 divided by the greatest perfect square from the list of all factors of 64800. We determined above that the greatest perfect square from the list of all factors of 64800 is 32400. Furthermore, 64800 divided by 32400 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 64800 in its simplest radical form as follows:

√64800 = A√B

√64800 = 180√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64800 to simplify the square root of 64800 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 64800 and then take the square root of that product. The prime factors that multiply together to make 64800 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 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 5 x 5 = 32400 and the square root of 32400 is 180. Therefore, A equals 180.

B = Divide 64800 by the number (A) squared. 180 squared is 32400 and 64800 divided by 32400 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 64800 in its simplest radical form as follows:

√64800 = A√B

√64800 = 180√2

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