Multiplication and Division of Radicals in General
Completion requirements
Multiplication and Division of Radicals in General
Multiplying and dividing radicals is straight forward. Coefficients can multiply/divide with other coefficients, and radicands can multiply/divide with other radicands as long as the index values are equal. Coefficients and radicands do not multiply/divide.
| Key Lesson Marker |
Multiplication of Radicals Rule
The rule for multiplying radicals is
\(a\) is the coefficient of the first radical
\(x\) is the radicand of the first radical
\(b\) is the coefficient of the second radical
\(y\) is the radicand of the second radical
\(c\) is the index of each radical
\[a\sqrt[c]{x} \cdot b\sqrt[c]{y} = ab\sqrt[c]{{xy}}\]
\(a\) is the coefficient of the first radical
\(x\) is the radicand of the first radical
\(b\) is the coefficient of the second radical
\(y\) is the radicand of the second radical
\(c\) is the index of each radical
| Key Lesson Marker |
Division of Radicals Rule
The rule for dividing radicals is
\(a\) is the coefficient of the radical in the numerator
\(x\) is the radicand of the radical in the numerator
\(b\) is the coefficient of the radical in the denominator
\(y\) is the radicand of the radical in the denominator
\(c\) is the index of each radical
\[
\frac{{a\sqrt[c]{x}}}{{b\sqrt[c]{y}}} = \frac{a}{b}\sqrt[c]{{\frac{x}{y}}}
\]
\frac{{a\sqrt[c]{x}}}{{b\sqrt[c]{y}}} = \frac{a}{b}\sqrt[c]{{\frac{x}{y}}}
\]
\(x\) is the radicand of the radical in the numerator
\(b\) is the coefficient of the radical in the denominator
\(y\) is the radicand of the radical in the denominator
\(c\) is the index of each radical