Simplify Square Root of 99873

Here we will show you two methods that you can use to simplify the square root of 99873. In other words, we will show you how to find the square root of 99873 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.

√99873 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99873 to simplify the square root of 99873. 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 99873. The factors of 99873 are 1, 3, 9, 27, 81, 137, 243, 411, 729, 1233, 3699, 11097, 33291, and 99873. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 99873 divided by the greatest perfect square from the list of all factors of 99873. We determined above that the greatest perfect square from the list of all factors of 99873 is 729. Furthermore, 99873 divided by 729 is 137, therefore B equals 137.

Now we have A and B and can get our answer to 99873 in its simplest radical form as follows:

√99873 = A√B

√99873 = 27√137

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99873 to simplify the square root of 99873 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 99873 and then take the square root of that product. The prime factors that multiply together to make 99873 are 3 x 3 x 3 x 3 x 3 x 3 x 137. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 99873 by the number (A) squared. 27 squared is 729 and 99873 divided by 729 is 137. Therefore, B equals 137.

Once again we have A and B and can get our answer to 99873 in its simplest radical form as follows:

√99873 = A√B

√99873 = 27√137

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Simplify Square Root of 99874
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