## anonymous 5 years ago I need help with adding and subtracting radicals! Anyone know how to do this??

1. anonymous

Give an example. Most of the time you can't do this explicitly, for example, sqrt(3) + sqrt(5) can't be rewritten in a simpler form.

2. anonymous

Alright, for example: $3\sqrt{20} + 7\sqrt{5}$ and one with a negative: $-2\sqrt{6} + 3\sqrt{54}$

3. anonymous

Oh ok. So the key here is that the numbers underneath the radical has factors which are square numbers. For example 20 = 4 * 5. But notice that 4 is a square number, since 4 = 2^2. And 54 = 6 * 9, so 54 has a factor which is a square, since 9 = 3^2. So in the first case, we can rewrite 3*sqrt(20) as 3*(sqrt(4 * 5)) = 3 *(sqrt(4) * sqrt(5)). But sqrt(4) = 2. So this becomes 3 * 2 * sqrt(5) = 6 sqrt(5) Now you can add 6 sqrt(5) with 7 sqrt(5) to get 13 sqrt(5). Try it with the other problem. I’ll skip steps, but you should get -2sqrt(6) + 9 sqrt(6) = 7 sqrt(6).

4. anonymous

Thank you!