Simplify Square Root of 91875

Here we will show you two methods that you can use to simplify the square root of 91875. In other words, we will show you how to find the square root of 91875 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.

√91875 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91875 to simplify the square root of 91875. 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 91875. The factors of 91875 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 125, 147, 175, 245, 375, 525, 625, 735, 875, 1225, 1875, 2625, 3675, 4375, 6125, 13125, 18375, 30625, and 91875. Furthermore, the greatest perfect square on this list is 30625 and the square root of 30625 is 175. Therefore, A equals 175.

B = Calculate 91875 divided by the greatest perfect square from the list of all factors of 91875. We determined above that the greatest perfect square from the list of all factors of 91875 is 30625. Furthermore, 91875 divided by 30625 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 91875 in its simplest radical form as follows:

√91875 = A√B

√91875 = 175√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91875 to simplify the square root of 91875 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 91875 and then take the square root of that product. The prime factors that multiply together to make 91875 are 3 x 5 x 5 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 5 x 5 x 5 x 5 x 7 x 7 = 30625 and the square root of 30625 is 175. Therefore, A equals 175.

B = Divide 91875 by the number (A) squared. 175 squared is 30625 and 91875 divided by 30625 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 91875 in its simplest radical form as follows:

√91875 = A√B

√91875 = 175√3

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