Simplify Square Root of 91854

Here we will show you two methods that you can use to simplify the square root of 91854. In other words, we will show you how to find the square root of 91854 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.

√91854 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91854 to simplify the square root of 91854. 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 91854. The factors of 91854 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 729, 1134, 1458, 1701, 2187, 3402, 4374, 5103, 6561, 10206, 13122, 15309, 30618, 45927, and 91854. Furthermore, the greatest perfect square on this list is 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Calculate 91854 divided by the greatest perfect square from the list of all factors of 91854. We determined above that the greatest perfect square from the list of all factors of 91854 is 6561. Furthermore, 91854 divided by 6561 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 91854 in its simplest radical form as follows:

√91854 = A√B

√91854 = 81√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91854 to simplify the square root of 91854 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 91854 and then take the square root of that product. The prime factors that multiply together to make 91854 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Divide 91854 by the number (A) squared. 81 squared is 6561 and 91854 divided by 6561 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 91854 in its simplest radical form as follows:

√91854 = A√B

√91854 = 81√14

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