Simplify: (picture) and can you show your work so that i can understand how to do it myself? you

We have to get the number inside the radicals to match up before we can add them together much like if they were fractions where the denominators must match before adding. 

Because they are square roots, we look for factors for the number inside the radical that repeat twice. In this case, the number inside the radical is 32. The factors of 32 are 2 and 16. 16 can be broken down into 4*4. So our factors will be 2*4*4 inside the radical. Any number without a match stays inside.

3√32 becomes 3√(4*4*2). Notice there are two 4's so we pull those out. This number becomes (3*4)√2 which simplifies to 12√2. Now since the number in the radicals match, we add the outside numbers like normal and the number inside the radical stays the same. 

12√2 + 6√2 is the same as (12 + 6)√2 which equals 18√2, the second option is your answer. 

3√32=
=3√4²×2=
=3√4²√2=
=3×4√2=
=12√2

12√2+6√2=
=18√2

Hope this helped!

If the diameter is 8 than the radius is 4 because 2r or 2*radius equals the diameter. 4*2=8. 8/2=4.