Simplify Square Root of 36180

Here we will show you two methods that you can use to simplify the square root of 36180. In other words, we will show you how to find the square root of 36180 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.

√36180 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36180 to simplify the square root of 36180. 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 36180. The factors of 36180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 67, 90, 108, 134, 135, 180, 201, 268, 270, 335, 402, 540, 603, 670, 804, 1005, 1206, 1340, 1809, 2010, 2412, 3015, 3618, 4020, 6030, 7236, 9045, 12060, 18090, and 36180. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 36180 divided by the greatest perfect square from the list of all factors of 36180. We determined above that the greatest perfect square from the list of all factors of 36180 is 36. Furthermore, 36180 divided by 36 is 1005, therefore B equals 1005.

Now we have A and B and can get our answer to 36180 in its simplest radical form as follows:

√36180 = A√B

√36180 = 6√1005

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36180 to simplify the square root of 36180 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 36180 and then take the square root of that product. The prime factors that multiply together to make 36180 are 2 x 2 x 3 x 3 x 3 x 5 x 67. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 36180 by the number (A) squared. 6 squared is 36 and 36180 divided by 36 is 1005. Therefore, B equals 1005.

Once again we have A and B and can get our answer to 36180 in its simplest radical form as follows:

√36180 = A√B

√36180 = 6√1005

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