Simplify Square Root of 12000

Here we will show you two methods that you can use to simplify the square root of 12000. In other words, we will show you how to find the square root of 12000 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.

√12000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12000 to simplify the square root of 12000. 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 12000. The factors of 12000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, and 12000. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 12000 divided by the greatest perfect square from the list of all factors of 12000. We determined above that the greatest perfect square from the list of all factors of 12000 is 400. Furthermore, 12000 divided by 400 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 12000 in its simplest radical form as follows:

√12000 = A√B

√12000 = 20√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12000 to simplify the square root of 12000 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 12000 and then take the square root of that product. The prime factors that multiply together to make 12000 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 12000 by the number (A) squared. 20 squared is 400 and 12000 divided by 400 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 12000 in its simplest radical form as follows:

√12000 = A√B

√12000 = 20√30

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Simplify Square Root of 12001
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