Simplify Square Root of 18297

Here we will show you two methods that you can use to simplify the square root of 18297. In other words, we will show you how to find the square root of 18297 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.

√18297 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18297 to simplify the square root of 18297. 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 18297. The factors of 18297 are 1, 3, 9, 19, 57, 107, 171, 321, 963, 2033, 6099, and 18297. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 18297 divided by the greatest perfect square from the list of all factors of 18297. We determined above that the greatest perfect square from the list of all factors of 18297 is 9. Furthermore, 18297 divided by 9 is 2033, therefore B equals 2033.

Now we have A and B and can get our answer to 18297 in its simplest radical form as follows:

√18297 = A√B

√18297 = 3√2033

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18297 to simplify the square root of 18297 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 18297 and then take the square root of that product. The prime factors that multiply together to make 18297 are 3 x 3 x 19 x 107. 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 18297 by the number (A) squared. 3 squared is 9 and 18297 divided by 9 is 2033. Therefore, B equals 2033.

Once again we have A and B and can get our answer to 18297 in its simplest radical form as follows:

√18297 = A√B

√18297 = 3√2033

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