Simplify Square Root of 37467

Here we will show you two methods that you can use to simplify the square root of 37467. In other words, we will show you how to find the square root of 37467 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.

√37467 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37467 to simplify the square root of 37467. 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 37467. The factors of 37467 are 1, 3, 9, 23, 69, 181, 207, 543, 1629, 4163, 12489, and 37467. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 37467 divided by the greatest perfect square from the list of all factors of 37467. We determined above that the greatest perfect square from the list of all factors of 37467 is 9. Furthermore, 37467 divided by 9 is 4163, therefore B equals 4163.

Now we have A and B and can get our answer to 37467 in its simplest radical form as follows:

√37467 = A√B

√37467 = 3√4163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37467 to simplify the square root of 37467 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 37467 and then take the square root of that product. The prime factors that multiply together to make 37467 are 3 x 3 x 23 x 181. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 37467 by the number (A) squared. 3 squared is 9 and 37467 divided by 9 is 4163. Therefore, B equals 4163.

Once again we have A and B and can get our answer to 37467 in its simplest radical form as follows:

√37467 = A√B

√37467 = 3√4163

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

Simplify Square Root of 37468
Here is the next square root on our list that we have simplifed for you.