Simplify Square Root of 37845

Here we will show you two methods that you can use to simplify the square root of 37845. In other words, we will show you how to find the square root of 37845 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.

√37845 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37845 to simplify the square root of 37845. 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 37845. The factors of 37845 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 841, 1305, 2523, 4205, 7569, 12615, and 37845. Furthermore, the greatest perfect square on this list is 7569 and the square root of 7569 is 87. Therefore, A equals 87.

B = Calculate 37845 divided by the greatest perfect square from the list of all factors of 37845. We determined above that the greatest perfect square from the list of all factors of 37845 is 7569. Furthermore, 37845 divided by 7569 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 37845 in its simplest radical form as follows:

√37845 = A√B

√37845 = 87√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37845 to simplify the square root of 37845 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 37845 and then take the square root of that product. The prime factors that multiply together to make 37845 are 3 x 3 x 5 x 29 x 29. When we strip out the pairs only, we get 3 x 3 x 29 x 29 = 7569 and the square root of 7569 is 87. Therefore, A equals 87.

B = Divide 37845 by the number (A) squared. 87 squared is 7569 and 37845 divided by 7569 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 37845 in its simplest radical form as follows:

√37845 = A√B

√37845 = 87√5

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

Simplify Square Root of 37846
Here is the next square root on our list that we have simplifed for you.