Simplify Square Root of 57629

Here we will show you two methods that you can use to simplify the square root of 57629. In other words, we will show you how to find the square root of 57629 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.

√57629 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57629 to simplify the square root of 57629. 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 57629. The factors of 57629 are 1, 11, 13, 31, 143, 169, 341, 403, 1859, 4433, 5239, and 57629. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 57629 divided by the greatest perfect square from the list of all factors of 57629. We determined above that the greatest perfect square from the list of all factors of 57629 is 169. Furthermore, 57629 divided by 169 is 341, therefore B equals 341.

Now we have A and B and can get our answer to 57629 in its simplest radical form as follows:

√57629 = A√B

√57629 = 13√341

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57629 to simplify the square root of 57629 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 57629 and then take the square root of that product. The prime factors that multiply together to make 57629 are 11 x 13 x 13 x 31. 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 57629 by the number (A) squared. 13 squared is 169 and 57629 divided by 169 is 341. Therefore, B equals 341.

Once again we have A and B and can get our answer to 57629 in its simplest radical form as follows:

√57629 = A√B

√57629 = 13√341

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

Simplify Square Root of 57630
Here is the next square root on our list that we have simplifed for you.