Algebra 2
Unit 1, Lesson 3: nth roots
Objectives
Unit
Skills
1-2
1-3
1-4
1-5
Students are able to evaluate perfect nth roots.
Students are able to estimate non-perfect nth roots and plot
them on a number line.
- Students are able to simplify nth roots (with numerical
radicands)
- Students are able to simplify nth roots (with variable
expression radicands).
Materials and Handouts
Homework
- Answer transparency for hw #1-2
#1-3
- Lesson 3 keynote presentation
More nth Roots
- Note-taking guide
Practice
- Classwork: Practice with nth roots worksheet
- Homework: More nth roots practice
Corrections to #12
Time
Activity
20 min Homework Check / Warm-up Activity
- Put the answers to hw #1-2 on the overhead. Students get one
point for each correct, and write their total at the top of
the page.
- When finished checking, they should begin the warm-up on
binder paper.
- As they are working, circulate to record grades and stamp
homework checkers.
- Discuss warm-up problems.
Discussion: What is an nth root?
30 min
- Show slides that ask students to determine the side lengths
for a perfect square and cube.
- Show slide illustrating how a square root or cube root can be
thought of as the length of a side of a square/cube with the
given area/volume.
- Show slide with a square with non-perfect area, along with a
number line. Students should work in groups to estimate the
side length and plot it on the number line. Repeat with a
non-perfect cube. Clarify how to position the side length on
the number line by thinking of proximity to the relative
areas/volumes.
- Show slide with number line and a few perfect and non-perfect
second and third roots. Ask students to draw a number line
and plot each number.
- Show slide that generalizes what an nth root is algebraically.
- Show slide that explains simplification by finding prime
factorization, with numerical radicands. Variable
expressions radicands will be modeled on the worksheet.
Individual Work
25 min
- Hand out the Practice with nth Roots sheet. Review on
overhead.
Closure
5 min
- Students:
o Write down homework in their logs/planners
o Self-assess on College Habits, filling in their logs
-
o
Report their grades out loud, one by one.
Algebra 2
Unit 1, Lesson 3: Lecture Notes
Period:
Name:
Main Concepts
Understanding Roots
121 ft2
512 ft3
Estimating Roots
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Evaluating Roots
Definition of nth root:
Simplifying Roots
To simplify an nth root, remove as many factors as possible from inside the
root.
Find the prime factorization and remove groups of factors based on
the index (the number in front of the root sign).
Algebra 2
Unit 1, Lesson 3: Classwork
Period:
Name:
Practice with nth Roots
Part 1: Evaluating Roots
Find the exact value of each root.
4
144
3
125
5
243
12
16
5
32
3
1000
3
1
343
Part 2: Estimating Roots
Estimate the side length of each shape, and plot it on the number line.
3 ft2
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Estimate the value of each root (to one decimal place), and plot it on the
number line.
50 
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4
61 
48 
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Part 3: Simplifying Roots – Numerical Expressions
Simplify each root completely.
3
72
3
250
300
4
810
Part 4: Simplifying Roots – Variable Expressions
Simplifying a root with a variable expression is done exactly the same way.
Read the example carefully.
Example Problem
Simplify
3
Work
 3 2  2  2  3  x 3  x1  y3  y3  z 2
4 6 2
24x y z
 2  x  y  y  3  x1  z 2
3
 2xy 2
 3xz 
3
2
Simplify each root completely.
12a3b8c
25xy10
Explanation
1) Write the prime
factorization of the
coefficient.
2) Split the variables
into groups based on
the index.
3) Remove groups of
factors from inside the
root, and simplify what
remains.
3
40x12 y2 z 7
3
64q3r6s9
Algebra 2
Homework #1-3
Period:
Name:
More nth Roots Practice
Part 1: Evaluating Roots
Find the exact value of each root.
3
400
4
512
8
10,000
256
Part 2: Estimating Roots
Estimate the value of each root (to one decimal place), and plot it on the
number line.
79 
3
3
100 
9
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5
Part 3: Simplifying Roots
Simplify each root completely.
3
6
216
3
375
4
6a4b6c8
6
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9
10