Simplify Square Root of 69775

Here we will show you two methods that you can use to simplify the square root of 69775. In other words, we will show you how to find the square root of 69775 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.

√69775 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69775 to simplify the square root of 69775. 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 69775. The factors of 69775 are 1, 5, 25, 2791, 13955, and 69775. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 69775 divided by the greatest perfect square from the list of all factors of 69775. We determined above that the greatest perfect square from the list of all factors of 69775 is 25. Furthermore, 69775 divided by 25 is 2791, therefore B equals 2791.

Now we have A and B and can get our answer to 69775 in its simplest radical form as follows:

√69775 = A√B

√69775 = 5√2791

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69775 to simplify the square root of 69775 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 69775 and then take the square root of that product. The prime factors that multiply together to make 69775 are 5 x 5 x 2791. 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 69775 by the number (A) squared. 5 squared is 25 and 69775 divided by 25 is 2791. Therefore, B equals 2791.

Once again we have A and B and can get our answer to 69775 in its simplest radical form as follows:

√69775 = A√B

√69775 = 5√2791

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

Simplify Square Root of 69776
Here is the next square root on our list that we have simplifed for you.