Simplify Square Root of 95256

Here we will show you two methods that you can use to simplify the square root of 95256. In other words, we will show you how to find the square root of 95256 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.

√95256 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95256 to simplify the square root of 95256. 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 95256. The factors of 95256 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 49, 54, 56, 63, 72, 81, 84, 98, 108, 126, 147, 162, 168, 189, 196, 216, 243, 252, 294, 324, 378, 392, 441, 486, 504, 567, 588, 648, 756, 882, 972, 1134, 1176, 1323, 1512, 1701, 1764, 1944, 2268, 2646, 3402, 3528, 3969, 4536, 5292, 6804, 7938, 10584, 11907, 13608, 15876, 23814, 31752, 47628, and 95256. Furthermore, the greatest perfect square on this list is 15876 and the square root of 15876 is 126. Therefore, A equals 126.

B = Calculate 95256 divided by the greatest perfect square from the list of all factors of 95256. We determined above that the greatest perfect square from the list of all factors of 95256 is 15876. Furthermore, 95256 divided by 15876 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 95256 in its simplest radical form as follows:

√95256 = A√B

√95256 = 126√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95256 to simplify the square root of 95256 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 95256 and then take the square root of that product. The prime factors that multiply together to make 95256 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7 = 15876 and the square root of 15876 is 126. Therefore, A equals 126.

B = Divide 95256 by the number (A) squared. 126 squared is 15876 and 95256 divided by 15876 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 95256 in its simplest radical form as follows:

√95256 = A√B

√95256 = 126√6

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