Simplify Square Root of 39780

Here we will show you two methods that you can use to simplify the square root of 39780. In other words, we will show you how to find the square root of 39780 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.

√39780 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39780 to simplify the square root of 39780. 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 39780. The factors of 39780 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 17, 18, 20, 26, 30, 34, 36, 39, 45, 51, 52, 60, 65, 68, 78, 85, 90, 102, 117, 130, 153, 156, 170, 180, 195, 204, 221, 234, 255, 260, 306, 340, 390, 442, 468, 510, 585, 612, 663, 765, 780, 884, 1020, 1105, 1170, 1326, 1530, 1989, 2210, 2340, 2652, 3060, 3315, 3978, 4420, 6630, 7956, 9945, 13260, 19890, and 39780. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 39780 divided by the greatest perfect square from the list of all factors of 39780. We determined above that the greatest perfect square from the list of all factors of 39780 is 36. Furthermore, 39780 divided by 36 is 1105, therefore B equals 1105.

Now we have A and B and can get our answer to 39780 in its simplest radical form as follows:

√39780 = A√B

√39780 = 6√1105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39780 to simplify the square root of 39780 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 39780 and then take the square root of that product. The prime factors that multiply together to make 39780 are 2 x 2 x 3 x 3 x 5 x 13 x 17. 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 39780 by the number (A) squared. 6 squared is 36 and 39780 divided by 36 is 1105. Therefore, B equals 1105.

Once again we have A and B and can get our answer to 39780 in its simplest radical form as follows:

√39780 = A√B

√39780 = 6√1105

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Simplify Square Root of 39781
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