1. Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu
Chabot Mathematics
§7.3 Factor Radicals
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. 7.3 Review § Any QUESTIONS About Any QUESTIONS About HomeWork
MTH 55
Review §
Any QUESTIONS About
§7.3 → Multiply Radicals
Any QUESTIONS About HomeWork
§7.3 → HW-26

3. Product Rule for Radicals
For any real numbers and
That is, The product of two nth roots is the nth root of the product of the two radicands.

4. Simplifying by Factoring
The number p is a perfect square if there exists a rational number q for which q2 = p. We say that p is a perfect nth power if qn = p for some rational number q.
The product rule allows us to simplify whenever ab contains a factor that is a perfect nth power

5. Simplify by Product Rule
Use The Product Rule in REVERSE to Facilitate the Simplification process
Note that and must both be real numbers

6. Simplify a Radical Expression with Index n by Factoring
Express the radicand as a product in which one factor is the largest perfect nth power possible.
Take the nth root of each factor
Simplification is complete when no radicand has a factor that is a perfect nth power.

7. Example  Simplify by Factoring
Simplify by factoring (assume x > 0)
a) b)
SOLUTION → Match INDICES
a) b)

8. Example  Simplify by Factoring
Simplify by factoring (assume x > 0)
a) b)
SOLN a) Note That the INDEX is 3

9. Example  Simplify by Factoring
Simplify by factoring (assume x > 0)
a) b)
SOLN b) Note INDEX of 5

10. Example  Simplify by Factoring
Simplify by factoring (assume x, y > 0)
a) b)
SOLN a) Note INDEX of 2

11. Example  Simplify by Factoring
Simplify by factoring (assume x, y > 0)
a) b)
SOLN b) Note INDEX of 3

12. Example  Simplify Simplify by factoring (assume w, z > 0)
SOLN: First perform Distribution
Note that all INDICES are common at 5

13. Example  Simplify SOLN: Use Radical Product Rule
SOLN: Use Commutative Property of Multiplication

14. Example  Simplify SOLN: Exponent Product Rule
SOLN: Next use Exponent POWER rule to expose as many bases as possible to the Power of 5; the Radical Index

15. Example  Simplify SOLN: Power-to-Power Exponent Rule
SOLN: Next Radical Product Rule

16. Example  Simplify SOLN: Perform 5th Root Operations
SOLN: Finally Factor GCF = wz2
ANS

17. WhiteBoard Work Problems From §7.3 Exercise Set
76, 80, 82, 92, 98
Adult Cardiac Index =

18. Exponent Rules are NOT Algebraic
All Done for Today
Exponent Rules are NOT Algebraic

19. Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu
Chabot Mathematics
Appendix
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer –

20. Graph y = |x|
Make T-table