Simplify Square Root of 40712

Here we will show you two methods that you can use to simplify the square root of 40712. In other words, we will show you how to find the square root of 40712 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.

√40712 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40712 to simplify the square root of 40712. 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 40712. The factors of 40712 are 1, 2, 4, 7, 8, 14, 28, 56, 727, 1454, 2908, 5089, 5816, 10178, 20356, and 40712. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 40712 divided by the greatest perfect square from the list of all factors of 40712. We determined above that the greatest perfect square from the list of all factors of 40712 is 4. Furthermore, 40712 divided by 4 is 10178, therefore B equals 10178.

Now we have A and B and can get our answer to 40712 in its simplest radical form as follows:

√40712 = A√B

√40712 = 2√10178

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40712 to simplify the square root of 40712 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 40712 and then take the square root of that product. The prime factors that multiply together to make 40712 are 2 x 2 x 2 x 7 x 727. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 40712 by the number (A) squared. 2 squared is 4 and 40712 divided by 4 is 10178. Therefore, B equals 10178.

Once again we have A and B and can get our answer to 40712 in its simplest radical form as follows:

√40712 = A√B

√40712 = 2√10178

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

Simplify Square Root of 40713
Here is the next square root on our list that we have simplifed for you.