Simplify Square Root of 63888

Here we will show you two methods that you can use to simplify the square root of 63888. In other words, we will show you how to find the square root of 63888 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.

√63888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63888 to simplify the square root of 63888. 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 63888. The factors of 63888 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 121, 132, 176, 242, 264, 363, 484, 528, 726, 968, 1331, 1452, 1936, 2662, 2904, 3993, 5324, 5808, 7986, 10648, 15972, 21296, 31944, and 63888. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 63888 divided by the greatest perfect square from the list of all factors of 63888. We determined above that the greatest perfect square from the list of all factors of 63888 is 1936. Furthermore, 63888 divided by 1936 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 63888 in its simplest radical form as follows:

√63888 = A√B

√63888 = 44√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63888 to simplify the square root of 63888 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 63888 and then take the square root of that product. The prime factors that multiply together to make 63888 are 2 x 2 x 2 x 2 x 3 x 11 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 63888 by the number (A) squared. 44 squared is 1936 and 63888 divided by 1936 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 63888 in its simplest radical form as follows:

√63888 = A√B

√63888 = 44√33

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