Absolute Value Rules
Algebra rules for absolute values are listed below.
Piecewise Definition: | \(\left| a \right| = \left\{ {\begin{array}{*{20}{c}}a&{{\rm{if}}\;a \ge 0}\\{ - a}&{{\rm{if}}\;a < 0}\end{array}} \right.\) | |
Square root definition: | \(\left| a \right| = \sqrt {{a^2}} \) | |
Rules: | 1. |–a| = |a| 2. |a| ≥ 0 3. Products: |ab| = |a||b| 4. Quotients: |a / b| = |a| / |b| 5. Powers: |a^{n}| = |a|^{n} 6. Triangle Inequality: 7. Alternate Triangle Inequality: | |
CAREFUL!! | Sums: |
See also
Absolute value of a complex number, triangle inequality (geometric)
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