Adding & Subtracting Radicals

Adding & Subtracting Radicals

1. It is a lot like adding and subtracting variables

   • Example: 2√3 + 5√3 = 7√3 This is like saying 2x + 5x = 7x
     • If they are not like terms we could not solve them this way.
       • For example, if it was 2√5 + 8√3 - They are not like terms so they cannot be combined. When adding radicals combine like radicals when you can.

2. Sometimes they don't seem to be radicals but they end up being able to be combined

   • Example: 2√3 + 4√12 -Notice that 4√12 is not in simplest form so, we need to simplify!
     • LETS SIMPLIFY 4√12 - 1st we have to factor 12. This will give you 4 & 3.
       • Now we have 4√4*3. The 4 inside will then pop out & become 2. In this step, you have to figure out the square root of the 4 inside which is 2. You would take the 2 out of the radical and place it where it is being multiplied by the 4 outside the radical.
         • Like this: 2*4√3. The last step to writing this in its simplest form is the following: You will simply multiply the 2*4=8. That 8 will then be the new number outside the radical. Making it 8√3.
           • NOW WE CAN SOLVE! So now we have 2√3 + 8√3 which when added equals 10√3. This is because 2+8=10 and we don't mess with the 3.

3. MORE TRICKY! √2 - √.1/2

   • 1st: Rewrite in simplest form because your are not suppose to have a fraction under the radical!
     • √2 - √1/2 - 2/2 - We have to multiply the number outside the radical by the fraction inside it. That would give you 4/2 or √2/√4
       • Now we have this: √2 - √2/√4 We would then simplify that down to √2 - √2/2
         • We would then write this as: 2√2/2 -√2/2 which would simplify down to 2√2 - √2 all over 2.
           • That would then gove us an answer of √2/2
           • REMEMBER WHEN YOU ADD OR SUBTRACT FRACTIONS YOU MUST FIND A COMMON DENOMINATOR > THAT IS THE SAME WHEN TALKING ABOuT RADICALS!