Simplify Square Root of 86400

Here we will show you two methods that you can use to simplify the square root of 86400. In other words, we will show you how to find the square root of 86400 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.

√86400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86400 to simplify the square root of 86400. 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 86400. The factors of 86400 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, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 384, 400, 432, 450, 480, 540, 576, 600, 640, 675, 720, 800, 864, 900, 960, 1080, 1152, 1200, 1350, 1440, 1600, 1728, 1800, 1920, 2160, 2400, 2700, 2880, 3200, 3456, 3600, 4320, 4800, 5400, 5760, 7200, 8640, 9600, 10800, 14400, 17280, 21600, 28800, 43200, and 86400. Furthermore, the greatest perfect square on this list is 14400 and the square root of 14400 is 120. Therefore, A equals 120.

B = Calculate 86400 divided by the greatest perfect square from the list of all factors of 86400. We determined above that the greatest perfect square from the list of all factors of 86400 is 14400. Furthermore, 86400 divided by 14400 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 86400 in its simplest radical form as follows:

√86400 = A√B

√86400 = 120√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86400 to simplify the square root of 86400 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 86400 and then take the square root of that product. The prime factors that multiply together to make 86400 are 2 x 2 x 2 x 2 x 2 x 2 x 2 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 2 x 2 x 3 x 3 x 5 x 5 = 14400 and the square root of 14400 is 120. Therefore, A equals 120.

B = Divide 86400 by the number (A) squared. 120 squared is 14400 and 86400 divided by 14400 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 86400 in its simplest radical form as follows:

√86400 = A√B

√86400 = 120√6

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