Simplify Square Root of 65007

Here we will show you two methods that you can use to simplify the square root of 65007. In other words, we will show you how to find the square root of 65007 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.

√65007 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65007 to simplify the square root of 65007. 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 65007. The factors of 65007 are 1, 3, 9, 31, 93, 233, 279, 699, 2097, 7223, 21669, and 65007. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 65007 divided by the greatest perfect square from the list of all factors of 65007. We determined above that the greatest perfect square from the list of all factors of 65007 is 9. Furthermore, 65007 divided by 9 is 7223, therefore B equals 7223.

Now we have A and B and can get our answer to 65007 in its simplest radical form as follows:

√65007 = A√B

√65007 = 3√7223

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65007 to simplify the square root of 65007 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 65007 and then take the square root of that product. The prime factors that multiply together to make 65007 are 3 x 3 x 31 x 233. 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 65007 by the number (A) squared. 3 squared is 9 and 65007 divided by 9 is 7223. Therefore, B equals 7223.

Once again we have A and B and can get our answer to 65007 in its simplest radical form as follows:

√65007 = A√B

√65007 = 3√7223

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

Simplify Square Root of 65008
Here is the next square root on our list that we have simplifed for you.