Simplify Square Root of 87856

Here we will show you two methods that you can use to simplify the square root of 87856. In other words, we will show you how to find the square root of 87856 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.

√87856 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87856 to simplify the square root of 87856. 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 87856. The factors of 87856 are 1, 2, 4, 8, 16, 17, 19, 34, 38, 68, 76, 136, 152, 272, 289, 304, 323, 578, 646, 1156, 1292, 2312, 2584, 4624, 5168, 5491, 10982, 21964, 43928, and 87856. Furthermore, the greatest perfect square on this list is 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Calculate 87856 divided by the greatest perfect square from the list of all factors of 87856. We determined above that the greatest perfect square from the list of all factors of 87856 is 4624. Furthermore, 87856 divided by 4624 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 87856 in its simplest radical form as follows:

√87856 = A√B

√87856 = 68√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87856 to simplify the square root of 87856 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 87856 and then take the square root of that product. The prime factors that multiply together to make 87856 are 2 x 2 x 2 x 2 x 17 x 17 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 17 x 17 = 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Divide 87856 by the number (A) squared. 68 squared is 4624 and 87856 divided by 4624 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 87856 in its simplest radical form as follows:

√87856 = A√B

√87856 = 68√19

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

Simplify Square Root of 87857
Here is the next square root on our list that we have simplifed for you.