Simplify Square Root of 39087

Here we will show you two methods that you can use to simplify the square root of 39087. In other words, we will show you how to find the square root of 39087 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.

√39087 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39087 to simplify the square root of 39087. 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 39087. The factors of 39087 are 1, 3, 9, 43, 101, 129, 303, 387, 909, 4343, 13029, and 39087. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 39087 divided by the greatest perfect square from the list of all factors of 39087. We determined above that the greatest perfect square from the list of all factors of 39087 is 9. Furthermore, 39087 divided by 9 is 4343, therefore B equals 4343.

Now we have A and B and can get our answer to 39087 in its simplest radical form as follows:

√39087 = A√B

√39087 = 3√4343

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39087 to simplify the square root of 39087 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 39087 and then take the square root of that product. The prime factors that multiply together to make 39087 are 3 x 3 x 43 x 101. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 39087 by the number (A) squared. 3 squared is 9 and 39087 divided by 9 is 4343. Therefore, B equals 4343.

Once again we have A and B and can get our answer to 39087 in its simplest radical form as follows:

√39087 = A√B

√39087 = 3√4343

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Simplify Square Root of 39088
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