Simplifying Radical Expressions: Combining Like Terms

1. Chabot Mathematics §7.4 +/−/Radicals Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. MTH 55 7.3 Review § • Any QUESTIONS About • §7.3 → Multiply Radicals • Any QUESTIONS About HomeWork • §7.3 → HW-33

3. Add & Subtract Radicals • Radical Expressions similar to those that follow can be simplified using the distributive property These cannot be combined.

4. CAVEAT Identical Indices • CAUTION • Only Radical Expressions with the SAME INDEX and SAME RADICAND may be combined • Expressions such as Those below CanNOT be simplified by Combining Terms

5. Example  Simplify by Add/Sub • Simplify by Adding or Subtracting a) b) • SOLN → chk 1st Indices & Radicands a) b)

6. Example  Simplify by Add/Sub • Simplify by Adding or Subtracting a) b) • SOLN → chk 1st Indices & Radicands a) Factor 28. Simplify. Combine like radicals. b)

7. Example  Simplify by Add/Sub • Simplify by Adding or Subtracting a) b) • SOLN → chk 1st Indices & Radicands a) Combine the like radicals by subtracting the coefficients and keeping the radical. b) Regroup terms.

8. Example  Simplify by Add/Sub • Simplify by Adding or Subtracting • SOLN → chk 1st Indices & Radicands

9. Example  Simplify by Add/Sub • Simplify by Adding or Subtracting (assume a, b > 0) • SOLN → Note that these are CUBE Rts

10. Radical Expression Division • Just as the root of a product can be expressed as the product of two roots, the root of a quotient can be expressed as the quotient of two roots.

11. Quotient Rule for Radicals • For any real numbers andwith b > 0 • Remember that an nth root is simplified when its radicand has no factors that are perfect nth pwrs • Recall also that we assume that no radicands represent negative quantities raised to an even power

12. Taking the square roots of the numerator & denominator Example  Simplify by Quotient • Simplify by taking roots of the numerator and denominator: a) b) • SOLN a)

13. Example  Simplify by Quotient • Simplify by taking roots of the numerator & denominator: b) • SOLN b) →

14. WhiteBoard Work • Problems From §7.4 Exercise Set • 10, 26, 28, 40, 56, 60, 84 • Recall Σ & Δ of Two Cubes • DIFFERENCE of Cubes: • a³ −b³ = (a−b)(a² + ab + b²) • SUM of Cubes: • a³ + b³ = (a + b)(a² −ab + b²)

15. All Done for Today AlbertEinstein • Born March 14, 1879 in Ulm, Württemberg, Germany • Died April 18, 1955 (age 76) in Princeton, New Jersey, USA

16. Chabot Mathematics Appendix Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu –

17. Graph y = |x| • Make T-table