Simplify Square Root of 37142

Here we will show you two methods that you can use to simplify the square root of 37142. In other words, we will show you how to find the square root of 37142 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.

√37142 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37142 to simplify the square root of 37142. 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 37142. The factors of 37142 are 1, 2, 7, 14, 49, 98, 379, 758, 2653, 5306, 18571, and 37142. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 37142 divided by the greatest perfect square from the list of all factors of 37142. We determined above that the greatest perfect square from the list of all factors of 37142 is 49. Furthermore, 37142 divided by 49 is 758, therefore B equals 758.

Now we have A and B and can get our answer to 37142 in its simplest radical form as follows:

√37142 = A√B

√37142 = 7√758

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37142 to simplify the square root of 37142 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 37142 and then take the square root of that product. The prime factors that multiply together to make 37142 are 2 x 7 x 7 x 379. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 37142 by the number (A) squared. 7 squared is 49 and 37142 divided by 49 is 758. Therefore, B equals 758.

Once again we have A and B and can get our answer to 37142 in its simplest radical form as follows:

√37142 = A√B

√37142 = 7√758

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

Simplify Square Root of 37143
Here is the next square root on our list that we have simplifed for you.