Simplify Square Root of 85950

Here we will show you two methods that you can use to simplify the square root of 85950. In other words, we will show you how to find the square root of 85950 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.

√85950 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85950 to simplify the square root of 85950. 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 85950. The factors of 85950 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 191, 225, 382, 450, 573, 955, 1146, 1719, 1910, 2865, 3438, 4775, 5730, 8595, 9550, 14325, 17190, 28650, 42975, and 85950. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 85950 divided by the greatest perfect square from the list of all factors of 85950. We determined above that the greatest perfect square from the list of all factors of 85950 is 225. Furthermore, 85950 divided by 225 is 382, therefore B equals 382.

Now we have A and B and can get our answer to 85950 in its simplest radical form as follows:

√85950 = A√B

√85950 = 15√382

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85950 to simplify the square root of 85950 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 85950 and then take the square root of that product. The prime factors that multiply together to make 85950 are 2 x 3 x 3 x 5 x 5 x 191. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 85950 by the number (A) squared. 15 squared is 225 and 85950 divided by 225 is 382. Therefore, B equals 382.

Once again we have A and B and can get our answer to 85950 in its simplest radical form as follows:

√85950 = A√B

√85950 = 15√382

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

Simplify Square Root of 85951
Here is the next square root on our list that we have simplifed for you.