Simplify Square Root of 32704

Here we will show you two methods that you can use to simplify the square root of 32704. In other words, we will show you how to find the square root of 32704 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.

√32704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32704 to simplify the square root of 32704. 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 32704. The factors of 32704 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 73, 112, 146, 224, 292, 448, 511, 584, 1022, 1168, 2044, 2336, 4088, 4672, 8176, 16352, and 32704. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 32704 divided by the greatest perfect square from the list of all factors of 32704. We determined above that the greatest perfect square from the list of all factors of 32704 is 64. Furthermore, 32704 divided by 64 is 511, therefore B equals 511.

Now we have A and B and can get our answer to 32704 in its simplest radical form as follows:

√32704 = A√B

√32704 = 8√511

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32704 to simplify the square root of 32704 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 32704 and then take the square root of that product. The prime factors that multiply together to make 32704 are 2 x 2 x 2 x 2 x 2 x 2 x 7 x 73. 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 32704 by the number (A) squared. 8 squared is 64 and 32704 divided by 64 is 511. Therefore, B equals 511.

Once again we have A and B and can get our answer to 32704 in its simplest radical form as follows:

√32704 = A√B

√32704 = 8√511

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

Simplify Square Root of 32705
Here is the next square root on our list that we have simplifed for you.