Simplify Square Root of 39688

Here we will show you two methods that you can use to simplify the square root of 39688. In other words, we will show you how to find the square root of 39688 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.

√39688 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39688 to simplify the square root of 39688. 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 39688. The factors of 39688 are 1, 2, 4, 8, 11, 22, 41, 44, 82, 88, 121, 164, 242, 328, 451, 484, 902, 968, 1804, 3608, 4961, 9922, 19844, and 39688. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 39688 divided by the greatest perfect square from the list of all factors of 39688. We determined above that the greatest perfect square from the list of all factors of 39688 is 484. Furthermore, 39688 divided by 484 is 82, therefore B equals 82.

Now we have A and B and can get our answer to 39688 in its simplest radical form as follows:

√39688 = A√B

√39688 = 22√82

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39688 to simplify the square root of 39688 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 39688 and then take the square root of that product. The prime factors that multiply together to make 39688 are 2 x 2 x 2 x 11 x 11 x 41. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 39688 by the number (A) squared. 22 squared is 484 and 39688 divided by 484 is 82. Therefore, B equals 82.

Once again we have A and B and can get our answer to 39688 in its simplest radical form as follows:

√39688 = A√B

√39688 = 22√82

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