Simplify Square Root of 85041

Here we will show you two methods that you can use to simplify the square root of 85041. In other words, we will show you how to find the square root of 85041 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.

√85041 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85041 to simplify the square root of 85041. 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 85041. The factors of 85041 are 1, 3, 9, 11, 33, 99, 859, 2577, 7731, 9449, 28347, and 85041. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 85041 divided by the greatest perfect square from the list of all factors of 85041. We determined above that the greatest perfect square from the list of all factors of 85041 is 9. Furthermore, 85041 divided by 9 is 9449, therefore B equals 9449.

Now we have A and B and can get our answer to 85041 in its simplest radical form as follows:

√85041 = A√B

√85041 = 3√9449

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85041 to simplify the square root of 85041 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 85041 and then take the square root of that product. The prime factors that multiply together to make 85041 are 3 x 3 x 11 x 859. 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 85041 by the number (A) squared. 3 squared is 9 and 85041 divided by 9 is 9449. Therefore, B equals 9449.

Once again we have A and B and can get our answer to 85041 in its simplest radical form as follows:

√85041 = A√B

√85041 = 3√9449

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 85042
Here is the next square root on our list that we have simplifed for you.