A. Adding and Subtracting Radicals
Completion requirements
A. Adding and Subtracting Radicals
In the Warm Up, you reviewed collecting like terms, and then simplifying polynomial expressions. Similarly, when adding and subtracting radicals, you will be collecting like radicals. Like radicals have the same index and the same radicand. Radicals can only be added and subtracted if they are like radicals. To add or subtract like radicals, simply add or subtract their coefficients.
Addition and Subtraction Rule
| Key Lesson Marker |
Addition and Subtraction Rule
The rule for adding or subtracting radicals is
\(a\sqrt[c]{x} \pm b\sqrt[c]{x} = \left( {a \pm b} \right)\sqrt[c]{x}\)
\(a\) is the coefficient of the first radical
\(b\) is the coefficient of the second radical
\(c\) is the index of each radical
\(x\) is the radicand of each radical
\(a\sqrt[c]{x} \pm b\sqrt[c]{x} = \left( {a \pm b} \right)\sqrt[c]{x}\)
\(a\) is the coefficient of the first radical
\(b\) is the coefficient of the second radical
\(c\) is the index of each radical
\(x\) is the radicand of each radical