Simplify Square Root of 40656

Here we will show you two methods that you can use to simplify the square root of 40656. In other words, we will show you how to find the square root of 40656 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.

√40656 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40656 to simplify the square root of 40656. 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 40656. The factors of 40656 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 56, 66, 77, 84, 88, 112, 121, 132, 154, 168, 176, 231, 242, 264, 308, 336, 363, 462, 484, 528, 616, 726, 847, 924, 968, 1232, 1452, 1694, 1848, 1936, 2541, 2904, 3388, 3696, 5082, 5808, 6776, 10164, 13552, 20328, and 40656. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 40656 divided by the greatest perfect square from the list of all factors of 40656. We determined above that the greatest perfect square from the list of all factors of 40656 is 1936. Furthermore, 40656 divided by 1936 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 40656 in its simplest radical form as follows:

√40656 = A√B

√40656 = 44√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40656 to simplify the square root of 40656 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 40656 and then take the square root of that product. The prime factors that multiply together to make 40656 are 2 x 2 x 2 x 2 x 3 x 7 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 40656 by the number (A) squared. 44 squared is 1936 and 40656 divided by 1936 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 40656 in its simplest radical form as follows:

√40656 = A√B

√40656 = 44√21

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