Unit 6.6 Radical Addition and Subtraction
Radical Addition and Subtraction
Radicals (or roots) can be added or subtracted if they are like radicals. Like radicals have the same radicand (the number under the radical) and the same index.
[latex]a\sqrt{x} + b\sqrt{x} = (a + b)\sqrt{x}[/latex]
Rules for Addition and Subtraction of Radicals
- Like Radicals: Combine the coefficients of the like radicals.
- Unlike Radicals: They cannot be simplified by addition or subtraction.
Example 1: Addition of Radicals
[latex]3\sqrt{5} + 2\sqrt{5} = (3 + 2)\sqrt{5} = 5\sqrt{5}[/latex]
Example 2: Addition of Radicals
[latex]5x\sqrt{y} - 2x\sqrt{y} - x\sqrt{y} = (5x - 2x - x)\sqrt{y} = 2x\sqrt{y}[/latex]