Simplify Square Root of 39690

Here we will show you two methods that you can use to simplify the square root of 39690. In other words, we will show you how to find the square root of 39690 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.

√39690 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39690 to simplify the square root of 39690. 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 39690. The factors of 39690 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 49, 54, 63, 70, 81, 90, 98, 105, 126, 135, 147, 162, 189, 210, 245, 270, 294, 315, 378, 405, 441, 490, 567, 630, 735, 810, 882, 945, 1134, 1323, 1470, 1890, 2205, 2646, 2835, 3969, 4410, 5670, 6615, 7938, 13230, 19845, and 39690. Furthermore, the greatest perfect square on this list is 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Calculate 39690 divided by the greatest perfect square from the list of all factors of 39690. We determined above that the greatest perfect square from the list of all factors of 39690 is 3969. Furthermore, 39690 divided by 3969 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 39690 in its simplest radical form as follows:

√39690 = A√B

√39690 = 63√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39690 to simplify the square root of 39690 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 39690 and then take the square root of that product. The prime factors that multiply together to make 39690 are 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 7 x 7 = 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Divide 39690 by the number (A) squared. 63 squared is 3969 and 39690 divided by 3969 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 39690 in its simplest radical form as follows:

√39690 = A√B

√39690 = 63√10

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Simplify Square Root of 39691
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