Simplify Square Root of 40300

Here we will show you two methods that you can use to simplify the square root of 40300. In other words, we will show you how to find the square root of 40300 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.

√40300 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40300 to simplify the square root of 40300. 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 40300. The factors of 40300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 31, 50, 52, 62, 65, 100, 124, 130, 155, 260, 310, 325, 403, 620, 650, 775, 806, 1300, 1550, 1612, 2015, 3100, 4030, 8060, 10075, 20150, and 40300. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 40300 divided by the greatest perfect square from the list of all factors of 40300. We determined above that the greatest perfect square from the list of all factors of 40300 is 100. Furthermore, 40300 divided by 100 is 403, therefore B equals 403.

Now we have A and B and can get our answer to 40300 in its simplest radical form as follows:

√40300 = A√B

√40300 = 10√403

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40300 to simplify the square root of 40300 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 40300 and then take the square root of that product. The prime factors that multiply together to make 40300 are 2 x 2 x 5 x 5 x 13 x 31. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 40300 by the number (A) squared. 10 squared is 100 and 40300 divided by 100 is 403. Therefore, B equals 403.

Once again we have A and B and can get our answer to 40300 in its simplest radical form as follows:

√40300 = A√B

√40300 = 10√403

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

Simplify Square Root of 40301
Here is the next square root on our list that we have simplifed for you.