Simplify Square Root of 39888

Here we will show you two methods that you can use to simplify the square root of 39888. In other words, we will show you how to find the square root of 39888 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.

√39888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39888 to simplify the square root of 39888. 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 39888. The factors of 39888 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277, 554, 831, 1108, 1662, 2216, 2493, 3324, 4432, 4986, 6648, 9972, 13296, 19944, and 39888. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 39888 divided by the greatest perfect square from the list of all factors of 39888. We determined above that the greatest perfect square from the list of all factors of 39888 is 144. Furthermore, 39888 divided by 144 is 277, therefore B equals 277.

Now we have A and B and can get our answer to 39888 in its simplest radical form as follows:

√39888 = A√B

√39888 = 12√277

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39888 to simplify the square root of 39888 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 39888 and then take the square root of that product. The prime factors that multiply together to make 39888 are 2 x 2 x 2 x 2 x 3 x 3 x 277. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 39888 by the number (A) squared. 12 squared is 144 and 39888 divided by 144 is 277. Therefore, B equals 277.

Once again we have A and B and can get our answer to 39888 in its simplest radical form as follows:

√39888 = A√B

√39888 = 12√277

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Simplify Square Root of 39889
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