Simplify Square Root of 39060

Here we will show you two methods that you can use to simplify the square root of 39060. In other words, we will show you how to find the square root of 39060 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.

√39060 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39060 to simplify the square root of 39060. 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 39060. The factors of 39060 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 31, 35, 36, 42, 45, 60, 62, 63, 70, 84, 90, 93, 105, 124, 126, 140, 155, 180, 186, 210, 217, 252, 279, 310, 315, 372, 420, 434, 465, 558, 620, 630, 651, 868, 930, 1085, 1116, 1260, 1302, 1395, 1860, 1953, 2170, 2604, 2790, 3255, 3906, 4340, 5580, 6510, 7812, 9765, 13020, 19530, and 39060. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 39060 divided by the greatest perfect square from the list of all factors of 39060. We determined above that the greatest perfect square from the list of all factors of 39060 is 36. Furthermore, 39060 divided by 36 is 1085, therefore B equals 1085.

Now we have A and B and can get our answer to 39060 in its simplest radical form as follows:

√39060 = A√B

√39060 = 6√1085

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39060 to simplify the square root of 39060 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 39060 and then take the square root of that product. The prime factors that multiply together to make 39060 are 2 x 2 x 3 x 3 x 5 x 7 x 31. 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 39060 by the number (A) squared. 6 squared is 36 and 39060 divided by 36 is 1085. Therefore, B equals 1085.

Once again we have A and B and can get our answer to 39060 in its simplest radical form as follows:

√39060 = A√B

√39060 = 6√1085

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Simplify Square Root of 39061
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