Simplify Square Root of 12800

Here we will show you two methods that you can use to simplify the square root of 12800. In other words, we will show you how to find the square root of 12800 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.

√12800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12800 to simplify the square root of 12800. 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 12800. The factors of 12800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1280, 1600, 2560, 3200, 6400, and 12800. Furthermore, the greatest perfect square on this list is 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Calculate 12800 divided by the greatest perfect square from the list of all factors of 12800. We determined above that the greatest perfect square from the list of all factors of 12800 is 6400. Furthermore, 12800 divided by 6400 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 12800 in its simplest radical form as follows:

√12800 = A√B

√12800 = 80√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12800 to simplify the square root of 12800 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 12800 and then take the square root of that product. The prime factors that multiply together to make 12800 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 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 2 x 2 x 5 x 5 = 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Divide 12800 by the number (A) squared. 80 squared is 6400 and 12800 divided by 6400 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 12800 in its simplest radical form as follows:

√12800 = A√B

√12800 = 80√2

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