Simplify Square Root of 84378

Here we will show you two methods that you can use to simplify the square root of 84378. In other words, we will show you how to find the square root of 84378 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.

√84378 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84378 to simplify the square root of 84378. 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 84378. The factors of 84378 are 1, 2, 3, 6, 7, 14, 21, 41, 42, 49, 82, 98, 123, 147, 246, 287, 294, 343, 574, 686, 861, 1029, 1722, 2009, 2058, 4018, 6027, 12054, 14063, 28126, 42189, and 84378. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 84378 divided by the greatest perfect square from the list of all factors of 84378. We determined above that the greatest perfect square from the list of all factors of 84378 is 49. Furthermore, 84378 divided by 49 is 1722, therefore B equals 1722.

Now we have A and B and can get our answer to 84378 in its simplest radical form as follows:

√84378 = A√B

√84378 = 7√1722

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84378 to simplify the square root of 84378 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 84378 and then take the square root of that product. The prime factors that multiply together to make 84378 are 2 x 3 x 7 x 7 x 7 x 41. 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 84378 by the number (A) squared. 7 squared is 49 and 84378 divided by 49 is 1722. Therefore, B equals 1722.

Once again we have A and B and can get our answer to 84378 in its simplest radical form as follows:

√84378 = A√B

√84378 = 7√1722

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

Simplify Square Root of 84379
Here is the next square root on our list that we have simplifed for you.