Simplify Square Root of 39208

Here we will show you two methods that you can use to simplify the square root of 39208. In other words, we will show you how to find the square root of 39208 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.

√39208 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39208 to simplify the square root of 39208. 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 39208. The factors of 39208 are 1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 169, 232, 338, 377, 676, 754, 1352, 1508, 3016, 4901, 9802, 19604, and 39208. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 39208 divided by the greatest perfect square from the list of all factors of 39208. We determined above that the greatest perfect square from the list of all factors of 39208 is 676. Furthermore, 39208 divided by 676 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 39208 in its simplest radical form as follows:

√39208 = A√B

√39208 = 26√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39208 to simplify the square root of 39208 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 39208 and then take the square root of that product. The prime factors that multiply together to make 39208 are 2 x 2 x 2 x 13 x 13 x 29. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 39208 by the number (A) squared. 26 squared is 676 and 39208 divided by 676 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 39208 in its simplest radical form as follows:

√39208 = A√B

√39208 = 26√58

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Simplify Square Root of 39209
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