MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Chabot Mathematics §7.4 +/−/ Radicals

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 2 Bruce Mayer, PE Chabot College Mathematics Review §  Any QUESTIONS About §7.3 → Multiply Radicals  Any QUESTIONS About HomeWork §7.3 → HW MTH 55

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 3 Bruce Mayer, PE Chabot College Mathematics Add & Subtract Radicals  Radical Expressions similar to those that follow can be simplified using the distributive property These canNOT be combined

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 4 Bruce Mayer, PE Chabot College Mathematics 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

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 5 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Add/Sub  Simplify by Adding or Subtracting a)b)  SOLN → chk 1 st Indices & Radicands a) b)

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 6 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Add/Sub  Simplify by Adding or Subtracting a)b)  SOLN → chk 1 st Indices & Radicands a) Factor 28. Combine like radicals. Simplify Radical b)

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 7 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Add/Sub  Simplify by Adding or Subtracting a)b)  SOLN → chk 1 st Indices & Radicands a) b) Combine the like radicals by subtracting the coefficients and keeping the radical. Regroup terms.

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 8 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Add/Sub  Simplify by Adding or Subtracting  SOLN → chk 1 st Indices & Radicands

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 9 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Add/Sub  Simplify by Adding or Subtracting (assume a, b > 0)  SOLN → Note that these are CUBE Rts

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 10 Bruce Mayer, PE Chabot College Mathematics 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.

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 11 Bruce Mayer, PE Chabot College Mathematics Quotient Rule for Radicals  For any real numbers and with b > 0  Remember that an n th root is simplified when its radicand has no factors that are perfect n th pwrs Recall also that we assume that no radicands represent negative quantities raised to an even power

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 12 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Quotient  Simplify by taking roots of the numerator and denominator: a)b)  SOLN a) Taking the square roots of the numerator & denominator

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 13 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Quotient  Simplify by taking roots of the numerator & denominator: b)  SOLN b) →

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 14 Bruce Mayer, PE Chabot College Mathematics 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 (a − b)(a² + ab + b²) SUM of Cubes: a³ + b³ = (a (a + b)(a² − ab + b²)

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 15 Bruce Mayer, PE Chabot College Mathematics All Done for Today Albert Einstein BBorn March 14, 1879 in Ulm, Württemberg, Germany DDied April 18, 1955 (age 76) in Princeton, New Jersey, USA

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 16 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Chabot Mathematics Appendix –

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 17 Bruce Mayer, PE Chabot College Mathematics Graph y = |x|  Make T-table

MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 18 Bruce Mayer, PE Chabot College Mathematics