Simplify Square Root of 39776

Here we will show you two methods that you can use to simplify the square root of 39776. In other words, we will show you how to find the square root of 39776 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.

√39776 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39776 to simplify the square root of 39776. 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 39776. The factors of 39776 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 113, 176, 226, 352, 452, 904, 1243, 1808, 2486, 3616, 4972, 9944, 19888, and 39776. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 39776 divided by the greatest perfect square from the list of all factors of 39776. We determined above that the greatest perfect square from the list of all factors of 39776 is 16. Furthermore, 39776 divided by 16 is 2486, therefore B equals 2486.

Now we have A and B and can get our answer to 39776 in its simplest radical form as follows:

√39776 = A√B

√39776 = 4√2486

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39776 to simplify the square root of 39776 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 39776 and then take the square root of that product. The prime factors that multiply together to make 39776 are 2 x 2 x 2 x 2 x 2 x 11 x 113. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 39776 by the number (A) squared. 4 squared is 16 and 39776 divided by 16 is 2486. Therefore, B equals 2486.

Once again we have A and B and can get our answer to 39776 in its simplest radical form as follows:

√39776 = A√B

√39776 = 4√2486

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Simplify Square Root of 39777
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