Simplify Square Root of 40729

Here we will show you two methods that you can use to simplify the square root of 40729. In other words, we will show you how to find the square root of 40729 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.

√40729 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40729 to simplify the square root of 40729. 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 40729. The factors of 40729 are 1, 13, 169, 241, 3133, and 40729. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 40729 divided by the greatest perfect square from the list of all factors of 40729. We determined above that the greatest perfect square from the list of all factors of 40729 is 169. Furthermore, 40729 divided by 169 is 241, therefore B equals 241.

Now we have A and B and can get our answer to 40729 in its simplest radical form as follows:

√40729 = A√B

√40729 = 13√241

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40729 to simplify the square root of 40729 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 40729 and then take the square root of that product. The prime factors that multiply together to make 40729 are 13 x 13 x 241. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 40729 by the number (A) squared. 13 squared is 169 and 40729 divided by 169 is 241. Therefore, B equals 241.

Once again we have A and B and can get our answer to 40729 in its simplest radical form as follows:

√40729 = A√B

√40729 = 13√241

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

Simplify Square Root of 40730
Here is the next square root on our list that we have simplifed for you.