Simplify Square Root of 39824

Here we will show you two methods that you can use to simplify the square root of 39824. In other words, we will show you how to find the square root of 39824 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.

√39824 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39824 to simplify the square root of 39824. 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 39824. The factors of 39824 are 1, 2, 4, 8, 16, 19, 38, 76, 131, 152, 262, 304, 524, 1048, 2096, 2489, 4978, 9956, 19912, and 39824. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 39824 divided by the greatest perfect square from the list of all factors of 39824. We determined above that the greatest perfect square from the list of all factors of 39824 is 16. Furthermore, 39824 divided by 16 is 2489, therefore B equals 2489.

Now we have A and B and can get our answer to 39824 in its simplest radical form as follows:

√39824 = A√B

√39824 = 4√2489

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39824 to simplify the square root of 39824 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 39824 and then take the square root of that product. The prime factors that multiply together to make 39824 are 2 x 2 x 2 x 2 x 19 x 131. 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 39824 by the number (A) squared. 4 squared is 16 and 39824 divided by 16 is 2489. Therefore, B equals 2489.

Once again we have A and B and can get our answer to 39824 in its simplest radical form as follows:

√39824 = A√B

√39824 = 4√2489

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