1. Radicals Roots of Real Numbers (7
Radicals Roots of Real Numbers (7.4) Products & Quotients of Radicals (7.5)
Target Goals: Simplify radicals having various indices; use a calculator to estimate roots of numbers; simplify radical expressions using multiplication & division; rationalize the denominator of a fraction containing a radical expression

2. Radicals  not just square roots!
Radical Sign
Index
Radicand
(the number under the radical sign)

3. b = radicand n = index b > 0 b < 0 b = 0 n is even
2 real roots: + & -
No real root
n is odd
1 + real roots
1 – real root

4. SIMPLIFYING RADICAL EXPRESSIONS
A radical expression is in simplified form when the following conditions are met:
The index is as small as possible. ***
The radicand contains no factors (other than 1) that are the nth powers of an integer or polynomial.
The radicand contains no fractions.
No radicals appear in the denominator.

5. PRODUCT PROPERTY OF RADICALS

6. QUOTIENT PROPERTY OF RADICALS

7. Ex 1) Find the following/Simplify:

8. Ex 2) Find the following/simplify

9. Ex 3) Find the following using your calculator:
Calculator Tips:
For cubed roots/index = 3
“MATH” button, option “4”
For indices larger than 3
* On the home screen, press the index #
* “MATH” button, option “5”

10. Ex 4) Simplify:

11. Ex 5) Simplify:

12. Ex 6) Simplify:

13. Ex 7) Simplify:

14. Ex 8) Simplify:

15. Ex 9) Simplify: