Simplify Square Root of 39377

Here we will show you two methods that you can use to simplify the square root of 39377. In other words, we will show you how to find the square root of 39377 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.

√39377 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39377 to simplify the square root of 39377. 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 39377. The factors of 39377 are 1, 13, 169, 233, 3029, and 39377. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 39377 divided by the greatest perfect square from the list of all factors of 39377. We determined above that the greatest perfect square from the list of all factors of 39377 is 169. Furthermore, 39377 divided by 169 is 233, therefore B equals 233.

Now we have A and B and can get our answer to 39377 in its simplest radical form as follows:

√39377 = A√B

√39377 = 13√233

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39377 to simplify the square root of 39377 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 39377 and then take the square root of that product. The prime factors that multiply together to make 39377 are 13 x 13 x 233. 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 39377 by the number (A) squared. 13 squared is 169 and 39377 divided by 169 is 233. Therefore, B equals 233.

Once again we have A and B and can get our answer to 39377 in its simplest radical form as follows:

√39377 = A√B

√39377 = 13√233

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

Simplify Square Root of 39378
Here is the next square root on our list that we have simplifed for you.