Simplify Square Root of 81297

Here we will show you two methods that you can use to simplify the square root of 81297. In other words, we will show you how to find the square root of 81297 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.

√81297 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81297 to simplify the square root of 81297. 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 81297. The factors of 81297 are 1, 3, 9, 27, 3011, 9033, 27099, and 81297. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 81297 divided by the greatest perfect square from the list of all factors of 81297. We determined above that the greatest perfect square from the list of all factors of 81297 is 9. Furthermore, 81297 divided by 9 is 9033, therefore B equals 9033.

Now we have A and B and can get our answer to 81297 in its simplest radical form as follows:

√81297 = A√B

√81297 = 3√9033

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81297 to simplify the square root of 81297 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 81297 and then take the square root of that product. The prime factors that multiply together to make 81297 are 3 x 3 x 3 x 3011. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 81297 by the number (A) squared. 3 squared is 9 and 81297 divided by 9 is 9033. Therefore, B equals 9033.

Once again we have A and B and can get our answer to 81297 in its simplest radical form as follows:

√81297 = A√B

√81297 = 3√9033

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Simplify Square Root of 81298
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