Simplify Square Root of 12032

Here we will show you two methods that you can use to simplify the square root of 12032. In other words, we will show you how to find the square root of 12032 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.

√12032 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12032 to simplify the square root of 12032. 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 12032. The factors of 12032 are 1, 2, 4, 8, 16, 32, 47, 64, 94, 128, 188, 256, 376, 752, 1504, 3008, 6016, and 12032. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 12032 divided by the greatest perfect square from the list of all factors of 12032. We determined above that the greatest perfect square from the list of all factors of 12032 is 256. Furthermore, 12032 divided by 256 is 47, therefore B equals 47.

Now we have A and B and can get our answer to 12032 in its simplest radical form as follows:

√12032 = A√B

√12032 = 16√47

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12032 to simplify the square root of 12032 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 12032 and then take the square root of that product. The prime factors that multiply together to make 12032 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 12032 by the number (A) squared. 16 squared is 256 and 12032 divided by 256 is 47. Therefore, B equals 47.

Once again we have A and B and can get our answer to 12032 in its simplest radical form as follows:

√12032 = A√B

√12032 = 16√47

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Simplify Square Root of 12033
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