Simplify Square Root of 34001

Here we will show you two methods that you can use to simplify the square root of 34001. In other words, we will show you how to find the square root of 34001 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.

√34001 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34001 to simplify the square root of 34001. 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 34001. The factors of 34001 are 1, 11, 121, 281, 3091, and 34001. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 34001 divided by the greatest perfect square from the list of all factors of 34001. We determined above that the greatest perfect square from the list of all factors of 34001 is 121. Furthermore, 34001 divided by 121 is 281, therefore B equals 281.

Now we have A and B and can get our answer to 34001 in its simplest radical form as follows:

√34001 = A√B

√34001 = 11√281

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34001 to simplify the square root of 34001 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 34001 and then take the square root of that product. The prime factors that multiply together to make 34001 are 11 x 11 x 281. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 34001 by the number (A) squared. 11 squared is 121 and 34001 divided by 121 is 281. Therefore, B equals 281.

Once again we have A and B and can get our answer to 34001 in its simplest radical form as follows:

√34001 = A√B

√34001 = 11√281

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

Simplify Square Root of 34002
Here is the next square root on our list that we have simplifed for you.