Simplify Square Root of 33456

Here we will show you two methods that you can use to simplify the square root of 33456. In other words, we will show you how to find the square root of 33456 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.

√33456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33456 to simplify the square root of 33456. 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 33456. The factors of 33456 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 41, 48, 51, 68, 82, 102, 123, 136, 164, 204, 246, 272, 328, 408, 492, 656, 697, 816, 984, 1394, 1968, 2091, 2788, 4182, 5576, 8364, 11152, 16728, and 33456. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 33456 divided by the greatest perfect square from the list of all factors of 33456. We determined above that the greatest perfect square from the list of all factors of 33456 is 16. Furthermore, 33456 divided by 16 is 2091, therefore B equals 2091.

Now we have A and B and can get our answer to 33456 in its simplest radical form as follows:

√33456 = A√B

√33456 = 4√2091

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33456 to simplify the square root of 33456 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 33456 and then take the square root of that product. The prime factors that multiply together to make 33456 are 2 x 2 x 2 x 2 x 3 x 17 x 41. 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 33456 by the number (A) squared. 4 squared is 16 and 33456 divided by 16 is 2091. Therefore, B equals 2091.

Once again we have A and B and can get our answer to 33456 in its simplest radical form as follows:

√33456 = A√B

√33456 = 4√2091

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 33457
Here is the next square root on our list that we have simplifed for you.