Simplify Square Root of 47104

Here we will show you two methods that you can use to simplify the square root of 47104. In other words, we will show you how to find the square root of 47104 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.

√47104 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47104 to simplify the square root of 47104. 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 47104. The factors of 47104 are 1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 128, 184, 256, 368, 512, 736, 1024, 1472, 2048, 2944, 5888, 11776, 23552, and 47104. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 47104 divided by the greatest perfect square from the list of all factors of 47104. We determined above that the greatest perfect square from the list of all factors of 47104 is 1024. Furthermore, 47104 divided by 1024 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 47104 in its simplest radical form as follows:

√47104 = A√B

√47104 = 32√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47104 to simplify the square root of 47104 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 47104 and then take the square root of that product. The prime factors that multiply together to make 47104 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Divide 47104 by the number (A) squared. 32 squared is 1024 and 47104 divided by 1024 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 47104 in its simplest radical form as follows:

√47104 = A√B

√47104 = 32√46

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

Simplify Square Root of 47105
Here is the next square root on our list that we have simplifed for you.