Simplify Square Root of 97281

Here we will show you two methods that you can use to simplify the square root of 97281. In other words, we will show you how to find the square root of 97281 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.

√97281 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97281 to simplify the square root of 97281. 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 97281. The factors of 97281 are 1, 3, 9, 27, 81, 1201, 3603, 10809, 32427, and 97281. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 97281 divided by the greatest perfect square from the list of all factors of 97281. We determined above that the greatest perfect square from the list of all factors of 97281 is 81. Furthermore, 97281 divided by 81 is 1201, therefore B equals 1201.

Now we have A and B and can get our answer to 97281 in its simplest radical form as follows:

√97281 = A√B

√97281 = 9√1201

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97281 to simplify the square root of 97281 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 97281 and then take the square root of that product. The prime factors that multiply together to make 97281 are 3 x 3 x 3 x 3 x 1201. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 97281 by the number (A) squared. 9 squared is 81 and 97281 divided by 81 is 1201. Therefore, B equals 1201.

Once again we have A and B and can get our answer to 97281 in its simplest radical form as follows:

√97281 = A√B

√97281 = 9√1201

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Simplify Square Root of 97282
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