Simplify Square Root of 23232

Here we will show you two methods that you can use to simplify the square root of 23232. In other words, we will show you how to find the square root of 23232 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.

√23232 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23232 to simplify the square root of 23232. 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 23232. The factors of 23232 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 121, 132, 176, 192, 242, 264, 352, 363, 484, 528, 704, 726, 968, 1056, 1452, 1936, 2112, 2904, 3872, 5808, 7744, 11616, and 23232. Furthermore, the greatest perfect square on this list is 7744 and the square root of 7744 is 88. Therefore, A equals 88.

B = Calculate 23232 divided by the greatest perfect square from the list of all factors of 23232. We determined above that the greatest perfect square from the list of all factors of 23232 is 7744. Furthermore, 23232 divided by 7744 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 23232 in its simplest radical form as follows:

√23232 = A√B

√23232 = 88√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23232 to simplify the square root of 23232 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 23232 and then take the square root of that product. The prime factors that multiply together to make 23232 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11 = 7744 and the square root of 7744 is 88. Therefore, A equals 88.

B = Divide 23232 by the number (A) squared. 88 squared is 7744 and 23232 divided by 7744 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 23232 in its simplest radical form as follows:

√23232 = A√B

√23232 = 88√3

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

Simplify Square Root of 23233
Here is the next square root on our list that we have simplifed for you.