Simplify Square Root of 94896

Here we will show you two methods that you can use to simplify the square root of 94896. In other words, we will show you how to find the square root of 94896 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.

√94896 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 94896 to simplify the square root of 94896. 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 94896. The factors of 94896 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 659, 1318, 1977, 2636, 3954, 5272, 5931, 7908, 10544, 11862, 15816, 23724, 31632, 47448, and 94896. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 94896 divided by the greatest perfect square from the list of all factors of 94896. We determined above that the greatest perfect square from the list of all factors of 94896 is 144. Furthermore, 94896 divided by 144 is 659, therefore B equals 659.

Now we have A and B and can get our answer to 94896 in its simplest radical form as follows:

√94896 = A√B

√94896 = 12√659

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 94896 to simplify the square root of 94896 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 94896 and then take the square root of that product. The prime factors that multiply together to make 94896 are 2 x 2 x 2 x 2 x 3 x 3 x 659. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 94896 by the number (A) squared. 12 squared is 144 and 94896 divided by 144 is 659. Therefore, B equals 659.

Once again we have A and B and can get our answer to 94896 in its simplest radical form as follows:

√94896 = A√B

√94896 = 12√659

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