Simplify Square Root of 32912




Here we will show you two methods that you can use to simplify the square root of 32912. In other words, we will show you how to find the square root of 32912 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.

32912 = A√B




Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32912 to simplify the square root of 32912. 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 32912. The factors of 32912 are 1, 2, 4, 8, 11, 16, 17, 22, 34, 44, 68, 88, 121, 136, 176, 187, 242, 272, 374, 484, 748, 968, 1496, 1936, 2057, 2992, 4114, 8228, 16456, and 32912. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 32912 divided by the greatest perfect square from the list of all factors of 32912. We determined above that the greatest perfect square from the list of all factors of 32912 is 1936. Furthermore, 32912 divided by 1936 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 32912 in its simplest radical form as follows:

32912 = A√B

32912 = 44√17




Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32912 to simplify the square root of 32912 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 32912 and then take the square root of that product. The prime factors that multiply together to make 32912 are 2 x 2 x 2 x 2 x 11 x 11 x 17. 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 32912 by the number (A) squared. 44 squared is 1936 and 32912 divided by 1936 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 32912 in its simplest radical form as follows:

32912 = A√B

32912 = 44√17



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




Simplify Square Root of 32913
Here is the next square root on our list that we have simplifed for you.


Copyright  |   Privacy Policy  |   Disclaimer  |   Contact