Simplify Square Root of 40256

Here we will show you two methods that you can use to simplify the square root of 40256. In other words, we will show you how to find the square root of 40256 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.

√40256 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40256 to simplify the square root of 40256. 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 40256. The factors of 40256 are 1, 2, 4, 8, 16, 17, 32, 34, 37, 64, 68, 74, 136, 148, 272, 296, 544, 592, 629, 1088, 1184, 1258, 2368, 2516, 5032, 10064, 20128, and 40256. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 40256 divided by the greatest perfect square from the list of all factors of 40256. We determined above that the greatest perfect square from the list of all factors of 40256 is 64. Furthermore, 40256 divided by 64 is 629, therefore B equals 629.

Now we have A and B and can get our answer to 40256 in its simplest radical form as follows:

√40256 = A√B

√40256 = 8√629

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40256 to simplify the square root of 40256 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 40256 and then take the square root of that product. The prime factors that multiply together to make 40256 are 2 x 2 x 2 x 2 x 2 x 2 x 17 x 37. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 40256 by the number (A) squared. 8 squared is 64 and 40256 divided by 64 is 629. Therefore, B equals 629.

Once again we have A and B and can get our answer to 40256 in its simplest radical form as follows:

√40256 = A√B

√40256 = 8√629

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