Simplify Square Root of 65008

Here we will show you two methods that you can use to simplify the square root of 65008. In other words, we will show you how to find the square root of 65008 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.

√65008 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65008 to simplify the square root of 65008. 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 65008. The factors of 65008 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 239, 272, 478, 956, 1912, 3824, 4063, 8126, 16252, 32504, and 65008. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 65008 divided by the greatest perfect square from the list of all factors of 65008. We determined above that the greatest perfect square from the list of all factors of 65008 is 16. Furthermore, 65008 divided by 16 is 4063, therefore B equals 4063.

Now we have A and B and can get our answer to 65008 in its simplest radical form as follows:

√65008 = A√B

√65008 = 4√4063

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65008 to simplify the square root of 65008 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 65008 and then take the square root of that product. The prime factors that multiply together to make 65008 are 2 x 2 x 2 x 2 x 17 x 239. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 65008 by the number (A) squared. 4 squared is 16 and 65008 divided by 16 is 4063. Therefore, B equals 4063.

Once again we have A and B and can get our answer to 65008 in its simplest radical form as follows:

√65008 = A√B

√65008 = 4√4063

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

Simplify Square Root of 65009
Here is the next square root on our list that we have simplifed for you.