AFM
P.3 Radicals and Rational Exponents Notes
After writing your journal, turn to your group and take turns sharing your journal
entry. Then as a group, form a solid definition of a square root.
______________ is a number that is the square of a rational number.
-Does that exclude anything that is a decimal?
Square root in radical form:
Square root in exponent form:
Now think back to yesterday’s lesson on the properties of exponents. What is the
product to powers rule?
Groups
Use this rule and the square root in exponent form to help you understand the
Product Rule for Square Roots.
If a and b represent nonnegative real numbers, then …
√𝑎𝑏=
(hint: start by putting it in “Exponent Form”)
Therefore,
Quotient Rule for Square Roots:
√𝑎
√𝑏
=
Practice Problems:
Evaluate:
1) √36
2) √100
3) √−100
Simplify the expression
1) √125𝑥 2
2) √6𝑥√3𝑥 2
3)
√200𝑥 3
√10𝑥 −1
Adding and Subtracting Like Radicals:
-Remember COMBINE LIKE TERMS!!!!!!
What if they are not like radicals?
1) 7√3 + √12
2) √50𝑥 − √8𝑥
Rationalizing the Denominator
You CANNOT have a radical in the denominator of a fraction!
1)
2)
3)
1
√7
3
3+√7
7
√5−2
Product and Quotient Rules for nth Roots:
Examples:
Rational Exponents:
Examples: