Simplify Square Root of 97792

Here we will show you two methods that you can use to simplify the square root of 97792. In other words, we will show you how to find the square root of 97792 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.

√97792 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97792 to simplify the square root of 97792. 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 97792. The factors of 97792 are 1, 2, 4, 8, 16, 32, 64, 128, 191, 256, 382, 512, 764, 1528, 3056, 6112, 12224, 24448, 48896, and 97792. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 97792 divided by the greatest perfect square from the list of all factors of 97792. We determined above that the greatest perfect square from the list of all factors of 97792 is 256. Furthermore, 97792 divided by 256 is 382, therefore B equals 382.

Now we have A and B and can get our answer to 97792 in its simplest radical form as follows:

√97792 = A√B

√97792 = 16√382

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97792 to simplify the square root of 97792 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 97792 and then take the square root of that product. The prime factors that multiply together to make 97792 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 191. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 97792 by the number (A) squared. 16 squared is 256 and 97792 divided by 256 is 382. Therefore, B equals 382.

Once again we have A and B and can get our answer to 97792 in its simplest radical form as follows:

√97792 = A√B

√97792 = 16√382

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