Simplify Square Root of 88218

Here we will show you two methods that you can use to simplify the square root of 88218. In other words, we will show you how to find the square root of 88218 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.

√88218 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88218 to simplify the square root of 88218. 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 88218. The factors of 88218 are 1, 2, 3, 6, 9, 13, 18, 26, 29, 39, 58, 78, 87, 117, 169, 174, 234, 261, 338, 377, 507, 522, 754, 1014, 1131, 1521, 2262, 3042, 3393, 4901, 6786, 9802, 14703, 29406, 44109, and 88218. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 88218 divided by the greatest perfect square from the list of all factors of 88218. We determined above that the greatest perfect square from the list of all factors of 88218 is 1521. Furthermore, 88218 divided by 1521 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 88218 in its simplest radical form as follows:

√88218 = A√B

√88218 = 39√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88218 to simplify the square root of 88218 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 88218 and then take the square root of that product. The prime factors that multiply together to make 88218 are 2 x 3 x 3 x 13 x 13 x 29. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 88218 by the number (A) squared. 39 squared is 1521 and 88218 divided by 1521 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 88218 in its simplest radical form as follows:

√88218 = A√B

√88218 = 39√58

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

Simplify Square Root of 88219
Here is the next square root on our list that we have simplifed for you.