1. Simplifying Radicals
Binomial Conjugate:
Binomial quantity that turns the expression
into a difference of squares.

2. Example 1 Binomials Conjugates

3. Example 2: Use Binomials Conjugates to Rationalize

4. The exponent is most often used in the power of monomials.
SPECIAL FRACTION EXPONENT:
The exponent is most often used in the power of monomials.
Examples: Do you notice any other type of mathematical symbols that these special fraction exponents represent?

5. Radicals: Steps for Simplifying Square Roots
Special Fraction Exponents, , are more commonly known as radicals in which the N value represents the root or index of the radical.
Index
Radical Symbol
Radicals:
Radicand
Note: The square root or ½ exponent is the most common radical and does not need to have the index written.
Steps for Simplifying Square Roots
Prime Factorization: Factor the Radicand Completely
Write the base of all perfect squares (PAIRS) outside of the radical as product
Everything else (SINGLES) stays under the radical as a product.

6. Operations with Rational (Fraction) Exponents
The same operations of when to multiply, add, subtract exponents apply with rational (fraction) exponents as did with integer (whole) exponents
Hint: Remember how to find common denominators and reduce. 1) 2) 3) 4) 5) 6)

7. Rational Exponents Property:
Radicals (Roots) and Rational Exponent Form
Rational Exponents Property: OR OR
Example 1: Change Rational to Radical Form A] B] C]
Example 2: Change Radical to Rational Form A] B] C]

8. Radicals Classwork # 1 – 4: Write in rational form. 1. 2. 3. 4.
#5 – 8: Write in radical form. 5. 6. 7. 8.

9. Determine if each pair are equivalent statements or not.
Radicals Classwork #2
Determine if each pair are equivalent statements or not. 1. 2.
and
and 3. 4.
and
and 5. 6.
and
and

10. Simplifying Rational Exponents
Apply normal operations with exponents.
Convert to radical form.
Simplify the radical expression based on the index and radicand. 1. 2. 3. 4. 5. 6. 7. 8.

11. Simplify the following expressions into simplest radical form
Radicals Classwork #3
Simplify the following expressions into simplest radical form 1. 2. 3. 6. 4. 5.

12. Change of Base (Index or Root)
Write the radicand in prime factorization form
REDUCE the fractions of Rational Exponents to rewrite radicals. 1. 2. 3. 3. 4. 3.

13. Change of Base Practice Problems1. 3. 2. 4. 5. 6.