Simplify Square Root of 39325

Here we will show you two methods that you can use to simplify the square root of 39325. In other words, we will show you how to find the square root of 39325 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.

√39325 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39325 to simplify the square root of 39325. 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 39325. The factors of 39325 are 1, 5, 11, 13, 25, 55, 65, 121, 143, 275, 325, 605, 715, 1573, 3025, 3575, 7865, and 39325. Furthermore, the greatest perfect square on this list is 3025 and the square root of 3025 is 55. Therefore, A equals 55.

B = Calculate 39325 divided by the greatest perfect square from the list of all factors of 39325. We determined above that the greatest perfect square from the list of all factors of 39325 is 3025. Furthermore, 39325 divided by 3025 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 39325 in its simplest radical form as follows:

√39325 = A√B

√39325 = 55√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39325 to simplify the square root of 39325 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 39325 and then take the square root of that product. The prime factors that multiply together to make 39325 are 5 x 5 x 11 x 11 x 13. When we strip out the pairs only, we get 5 x 5 x 11 x 11 = 3025 and the square root of 3025 is 55. Therefore, A equals 55.

B = Divide 39325 by the number (A) squared. 55 squared is 3025 and 39325 divided by 3025 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 39325 in its simplest radical form as follows:

√39325 = A√B

√39325 = 55√13

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Simplify Square Root of 39326
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