Simplify Square Root of 88056

Here we will show you two methods that you can use to simplify the square root of 88056. In other words, we will show you how to find the square root of 88056 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.

√88056 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88056 to simplify the square root of 88056. 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 88056. The factors of 88056 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 1223, 2446, 3669, 4892, 7338, 9784, 11007, 14676, 22014, 29352, 44028, and 88056. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 88056 divided by the greatest perfect square from the list of all factors of 88056. We determined above that the greatest perfect square from the list of all factors of 88056 is 36. Furthermore, 88056 divided by 36 is 2446, therefore B equals 2446.

Now we have A and B and can get our answer to 88056 in its simplest radical form as follows:

√88056 = A√B

√88056 = 6√2446

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88056 to simplify the square root of 88056 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 88056 and then take the square root of that product. The prime factors that multiply together to make 88056 are 2 x 2 x 2 x 3 x 3 x 1223. 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 88056 by the number (A) squared. 6 squared is 36 and 88056 divided by 36 is 2446. Therefore, B equals 2446.

Once again we have A and B and can get our answer to 88056 in its simplest radical form as follows:

√88056 = A√B

√88056 = 6√2446

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