1. 7.1 – Radicals Radical Expressions
Finding a root of a number is the inverse operation of raising a number to a power.
This symbol is the radical or the radical sign
radical sign
index
radicand
The expression under the radical sign is the radicand.
The index defines the root to be taken.

2. 7.1 – Radicals Radical Expressions
The above symbol represents the positive or principal root of a number.
The symbol represents the negative root of a number.

3. 7.1 – Radicals Square Roots
A square root of any positive number has two roots – one is positive and the other is negative.
If a is a positive number, then
is the positive square root of a and
is the negative square root of a.
Examples:
non-real #

4. 7.1 – Radicals Rdicals Cube Roots
A cube root of any positive number is positive.
A cube root of any negative number is negative.
Examples:

5. 7.1 – Radicals
nth Roots
An nth root of any number a is a number whose nth power is a.
Examples:

6. 7.1 – Radicals
nth Roots
An nth root of any number a is a number whose nth power is a.
Examples:
Non-real number
Non-real number

7. 7.2 – Rational Exponents
The value of the numerator represents the power of the radicand.
The value of the denominator represents the index or root of the expression.
Examples:

8. 7.2 – Rational Exponents
More Examples: or

9. 7.2 – Rational Exponents or or
Examples: or

10. 7.2 – Rational Exponents
Use the properties of exponents to simplify each expression

11. 7.3 – Simplifying Rational Expressions
Product Rule for Square Roots
Examples:

12. 7.3 – Simplifying Rational Expressions
Quotient Rule for Square Roots
Examples:

13. 7.3 – Simplifying Rational Expressions

14. 7.3 – Simplifying Rational Expressions
Examples:

15. 7.3 – Simplifying Rational Expressions
Examples:

16. 7.3 – Simplifying Rational Expressions
One Big Final Example

17. 7.4 – Adding, Subtracting, Multiplying Radical Expressions
Review and Examples:

18. 7.4 – Adding, Subtracting, Multiplying Radical Expressions
Simplifying Radicals Prior to Adding or Subtracting

19. 7.4 – Adding, Subtracting, Multiplying Radical Expressions
Simplifying Radicals Prior to Adding or Subtracting

20. 7.4 – Adding, Subtracting, Multiplying Radical Expressions

21. 7.4 – Adding, Subtracting, Multiplying Radical Expressions

22. 7.4 – Adding, Subtracting, Multiplying Radical Expressions