Simplify Square Root of 69725

Here we will show you two methods that you can use to simplify the square root of 69725. In other words, we will show you how to find the square root of 69725 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.

√69725 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69725 to simplify the square root of 69725. 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 69725. The factors of 69725 are 1, 5, 25, 2789, 13945, and 69725. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 69725 divided by the greatest perfect square from the list of all factors of 69725. We determined above that the greatest perfect square from the list of all factors of 69725 is 25. Furthermore, 69725 divided by 25 is 2789, therefore B equals 2789.

Now we have A and B and can get our answer to 69725 in its simplest radical form as follows:

√69725 = A√B

√69725 = 5√2789

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69725 to simplify the square root of 69725 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 69725 and then take the square root of that product. The prime factors that multiply together to make 69725 are 5 x 5 x 2789. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 69725 by the number (A) squared. 5 squared is 25 and 69725 divided by 25 is 2789. Therefore, B equals 2789.

Once again we have A and B and can get our answer to 69725 in its simplest radical form as follows:

√69725 = A√B

√69725 = 5√2789

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

Simplify Square Root of 69726
Here is the next square root on our list that we have simplifed for you.