Simplify Square Root of 94688

Here we will show you two methods that you can use to simplify the square root of 94688. In other words, we will show you how to find the square root of 94688 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.

√94688 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 94688 to simplify the square root of 94688. 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 94688. The factors of 94688 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 269, 352, 538, 1076, 2152, 2959, 4304, 5918, 8608, 11836, 23672, 47344, and 94688. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 94688 divided by the greatest perfect square from the list of all factors of 94688. We determined above that the greatest perfect square from the list of all factors of 94688 is 16. Furthermore, 94688 divided by 16 is 5918, therefore B equals 5918.

Now we have A and B and can get our answer to 94688 in its simplest radical form as follows:

√94688 = A√B

√94688 = 4√5918

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 94688 to simplify the square root of 94688 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 94688 and then take the square root of that product. The prime factors that multiply together to make 94688 are 2 x 2 x 2 x 2 x 2 x 11 x 269. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 94688 by the number (A) squared. 4 squared is 16 and 94688 divided by 16 is 5918. Therefore, B equals 5918.

Once again we have A and B and can get our answer to 94688 in its simplest radical form as follows:

√94688 = A√B

√94688 = 4√5918

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