Cogito
Algebra 2 · Chapter 5 · Lesson 1
Rational Exponents and Radical Equations
A fractional exponent is a root.
10 problems · about 20 minutes · N-RN.A.1, N-RN.A.2, A-REI.A.2
What this lesson teaches
The student converts between radical and rational exponent form and solves radical equations.
- A fractional exponent is a root; the denominator says which.
- The exponent laws carry over unchanged.
- Squaring both sides can invent solutions, so check them.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Direct, Inverse, and Joint Variation: y varies inversely with x, and y = 10 when x = 3. What is k?
Answer 30
Why 30.
Review — Adding and Simplifying Rational Expressions: (x² − 36)/(x − 6) simplifies to x + what?
Answer 6
Why x + 6.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is 81^(1/2)?
Answer 9
Why 9.
In x^(m/n), which number gives the root?
Answer The bottom one, n.
Why The denominator is the root.
What is 25^(1/2)?
Answer 5
Why Square root.
What is 8^(2/3)?
Answer 4
Why Cube root of 8 is 2, then squared.
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is 64^(1/3)?
Answer 4
Why Cube root.
Must you check answers after squaring both sides?
Answer Yes.
Why Squaring can invent solutions.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Exponent: What is 16^(1/2)?
Answer 4
Why 4.
The Cube Root: What is 27^(1/3)?
Answer 3
Why 3.