Simplify Square Root of 92565

Here we will show you two methods that you can use to simplify the square root of 92565. In other words, we will show you how to find the square root of 92565 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.

√92565 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92565 to simplify the square root of 92565. 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 92565. The factors of 92565 are 1, 3, 5, 9, 11, 15, 17, 33, 45, 51, 55, 85, 99, 121, 153, 165, 187, 255, 363, 495, 561, 605, 765, 935, 1089, 1683, 1815, 2057, 2805, 5445, 6171, 8415, 10285, 18513, 30855, and 92565. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 92565 divided by the greatest perfect square from the list of all factors of 92565. We determined above that the greatest perfect square from the list of all factors of 92565 is 1089. Furthermore, 92565 divided by 1089 is 85, therefore B equals 85.

Now we have A and B and can get our answer to 92565 in its simplest radical form as follows:

√92565 = A√B

√92565 = 33√85

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92565 to simplify the square root of 92565 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 92565 and then take the square root of that product. The prime factors that multiply together to make 92565 are 3 x 3 x 5 x 11 x 11 x 17. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 92565 by the number (A) squared. 33 squared is 1089 and 92565 divided by 1089 is 85. Therefore, B equals 85.

Once again we have A and B and can get our answer to 92565 in its simplest radical form as follows:

√92565 = A√B

√92565 = 33√85

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