Simplify Square Root of 18000

Here we will show you two methods that you can use to simplify the square root of 18000. In other words, we will show you how to find the square root of 18000 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.

√18000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18000 to simplify the square root of 18000. 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 18000. The factors of 18000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 125, 144, 150, 180, 200, 225, 240, 250, 300, 360, 375, 400, 450, 500, 600, 720, 750, 900, 1000, 1125, 1200, 1500, 1800, 2000, 2250, 3000, 3600, 4500, 6000, 9000, and 18000. Furthermore, the greatest perfect square on this list is 3600 and the square root of 3600 is 60. Therefore, A equals 60.

B = Calculate 18000 divided by the greatest perfect square from the list of all factors of 18000. We determined above that the greatest perfect square from the list of all factors of 18000 is 3600. Furthermore, 18000 divided by 3600 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 18000 in its simplest radical form as follows:

√18000 = A√B

√18000 = 60√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18000 to simplify the square root of 18000 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 18000 and then take the square root of that product. The prime factors that multiply together to make 18000 are 2 x 2 x 2 x 2 x 3 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 3 x 3 x 5 x 5 = 3600 and the square root of 3600 is 60. Therefore, A equals 60.

B = Divide 18000 by the number (A) squared. 60 squared is 3600 and 18000 divided by 3600 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 18000 in its simplest radical form as follows:

√18000 = A√B

√18000 = 60√5

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Simplify Square Root of 18001
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