Absolute value of real numbers and approximate calculation
See absolute value as distance from the origin, meet the three cases, compare |a + b| with |a| + |b|, and calculate with approximate roots.
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Guide
The absolute value of a, written |a|, is the distance of a from the origin. A distance is never negative, so |-2.5| = 2.5 and |2.5| = 2.5. This holds for any real number, even √5 and -√5.
Three cases: if a > 0 then |a| = a; if a = 0 then |a| = 0; if a < 0 then |a| = -a, which is positive.
Two properties: |a × b| = |a| × |b| and |a + b| ≤ |a| + |b|. The second is an equality only when a and b have the same sign.
With irrational numbers we use approximations: √2 ≈ 1.41 and √3 ≈ 1.73. The result is then approximate, and we write ≈.