Simplify Square Root of 19200

Here we will show you two methods that you can use to simplify the square root of 19200. In other words, we will show you how to find the square root of 19200 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.

√19200 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19200 to simplify the square root of 19200. 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 19200. The factors of 19200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 600, 640, 768, 800, 960, 1200, 1280, 1600, 1920, 2400, 3200, 3840, 4800, 6400, 9600, and 19200. Furthermore, the greatest perfect square on this list is 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Calculate 19200 divided by the greatest perfect square from the list of all factors of 19200. We determined above that the greatest perfect square from the list of all factors of 19200 is 6400. Furthermore, 19200 divided by 6400 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 19200 in its simplest radical form as follows:

√19200 = A√B

√19200 = 80√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19200 to simplify the square root of 19200 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 19200 and then take the square root of that product. The prime factors that multiply together to make 19200 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 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 2 x 2 x 5 x 5 = 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Divide 19200 by the number (A) squared. 80 squared is 6400 and 19200 divided by 6400 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 19200 in its simplest radical form as follows:

√19200 = A√B

√19200 = 80√3

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