Simplify Square Root of 48888

Here we will show you two methods that you can use to simplify the square root of 48888. In other words, we will show you how to find the square root of 48888 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.

√48888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48888 to simplify the square root of 48888. 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 48888. The factors of 48888 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 97, 126, 168, 194, 252, 291, 388, 504, 582, 679, 776, 873, 1164, 1358, 1746, 2037, 2328, 2716, 3492, 4074, 5432, 6111, 6984, 8148, 12222, 16296, 24444, and 48888. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 48888 divided by the greatest perfect square from the list of all factors of 48888. We determined above that the greatest perfect square from the list of all factors of 48888 is 36. Furthermore, 48888 divided by 36 is 1358, therefore B equals 1358.

Now we have A and B and can get our answer to 48888 in its simplest radical form as follows:

√48888 = A√B

√48888 = 6√1358

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48888 to simplify the square root of 48888 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 48888 and then take the square root of that product. The prime factors that multiply together to make 48888 are 2 x 2 x 2 x 3 x 3 x 7 x 97. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 48888 by the number (A) squared. 6 squared is 36 and 48888 divided by 36 is 1358. Therefore, B equals 1358.

Once again we have A and B and can get our answer to 48888 in its simplest radical form as follows:

√48888 = A√B

√48888 = 6√1358

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

Simplify Square Root of 48889
Here is the next square root on our list that we have simplifed for you.