Name: ______________________________________________ Date: _______________ Adv. Algebra II
6.1 – 6.3 Study Guide/Review
6.1 – Roots and Radical Expressions
Main Ideas: finding nth roots, real vs. imaginary roots, when to use absolute value symbols
Directions: Simplify each radical expression if possible. Use absolute value symbols
when needed.
1.
4
√96𝑥 5 𝑦 8
3
2.
√
8𝑥 4
5
3. √44𝑥 3 𝑧 5
216
6.2 – Multiplying and Dividing Radical Expressions
Main Ideas: combining radical expressions when multiplying or dividing (must have same
index), simplifying a radical expression, simplifying a product, rationalizing a denominator
Directions: Multiply or divide if possible. Then, simplify and rationalize the denominator.
Use absolute value if necessary.
4. √8𝑥 5 • √40𝑥 2
6.
√
36𝑥 3
𝑥5
4
4
5. √8𝑥 5 𝑦 4 • √32𝑥 3 𝑦
7.
3
9
√3𝑥 2 𝑦
Name: ______________________________________________ Date: _______________ Adv. Algebra II
8.
√5𝑥 4 𝑦
√2𝑥 2 𝑦 3
9.
3
√8 • √5
6.3 – Binomial Radical Expressions
Main Ideas: combining radical expressions when multiplying or dividing by using the distributive
property (must have the same index and radicand), simplifying before adding/subtracting,
multiplying binomial radical expressions (FOIL), conjugates of radical expressions, rationalizing
a denominator (by using conjugates)
Directions: Simplify as much as possible and rationalize the denominator. Assume all
variables are positive.
10. 5√32𝑥 + 4√98𝑥
13.
4+√6
√2+√3
12.
(√3 − √7)(√3 + 2√7)