Caddell Prep Access Menu

Adding and Subtracting Radical Expressions

In this video, we are going to add and subtract radical expressions.

We can add 3x+5x=8x
and we can do the same to 3\sqrt{2}+5\sqrt{2}=8\sqrt{2}

Since we can only combine like terms, we know that we cannot add 5x and 7y together
so we cannot add 5\sqrt{2} and 7\sqrt{3} together either

For 9\sqrt{6}+3\sqrt{5}-4\sqrt{6}+2\sqrt{5},
it would be 5\sqrt{6}+5\sqrt{5}

Let’s look at other examples:
3\sqrt{2}+6\sqrt{18}
3\sqrt{2} would stay like itself, while 6\sqrt{18} can be broken into 18\sqrt{2}
Now that both expressions are like terms, they can be combined into 21\sqrt{2}

6\sqrt{12}-4\sqrt{45}+2\sqrt{3}-\sqrt{80}
After simplifying each radical expression, it will be 12\sqrt{3}-12\sqrt{5}+2\sqrt{3}-4\sqrt{5}
After combining like terms, it will be 14\sqrt{3}-16\sqrt{5}