Simplify Square Root of 43628

Here we will show you two methods that you can use to simplify the square root of 43628. In other words, we will show you how to find the square root of 43628 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.

√43628 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43628 to simplify the square root of 43628. 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 43628. The factors of 43628 are 1, 2, 4, 13, 26, 52, 839, 1678, 3356, 10907, 21814, and 43628. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 43628 divided by the greatest perfect square from the list of all factors of 43628. We determined above that the greatest perfect square from the list of all factors of 43628 is 4. Furthermore, 43628 divided by 4 is 10907, therefore B equals 10907.

Now we have A and B and can get our answer to 43628 in its simplest radical form as follows:

√43628 = A√B

√43628 = 2√10907

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43628 to simplify the square root of 43628 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 43628 and then take the square root of that product. The prime factors that multiply together to make 43628 are 2 x 2 x 13 x 839. 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 43628 by the number (A) squared. 2 squared is 4 and 43628 divided by 4 is 10907. Therefore, B equals 10907.

Once again we have A and B and can get our answer to 43628 in its simplest radical form as follows:

√43628 = A√B

√43628 = 2√10907

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

Simplify Square Root of 43629
Here is the next square root on our list that we have simplifed for you.