Simplify Square Root of 91845

Here we will show you two methods that you can use to simplify the square root of 91845. In other words, we will show you how to find the square root of 91845 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.

√91845 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91845 to simplify the square root of 91845. 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 91845. The factors of 91845 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 157, 195, 471, 585, 785, 1413, 2041, 2355, 6123, 7065, 10205, 18369, 30615, and 91845. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 91845 divided by the greatest perfect square from the list of all factors of 91845. We determined above that the greatest perfect square from the list of all factors of 91845 is 9. Furthermore, 91845 divided by 9 is 10205, therefore B equals 10205.

Now we have A and B and can get our answer to 91845 in its simplest radical form as follows:

√91845 = A√B

√91845 = 3√10205

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91845 to simplify the square root of 91845 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 91845 and then take the square root of that product. The prime factors that multiply together to make 91845 are 3 x 3 x 5 x 13 x 157. 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 91845 by the number (A) squared. 3 squared is 9 and 91845 divided by 9 is 10205. Therefore, B equals 10205.

Once again we have A and B and can get our answer to 91845 in its simplest radical form as follows:

√91845 = A√B

√91845 = 3√10205

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