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Algebra 2 6-1 Complete Lesson: Roots and Radical Expressions

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Last updated over 4 years ago
32 questions
Note from the author:
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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
Question 1
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Question 2
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Question 3
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Question 4
4.

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Question 19
19.

Error Analysis: A student said the only fourth root of 16 is 2. Describe her error.

Question 21
21.

Reasoning: A number has only one real nth root. What can you conclude about the index n?

Question 22
22.

Question 23
23.

Review Lesson 4-7: Write the common form of the quadratic formula.
Hint: It shoud be in this format: x = [insert correct rational expression here].

Question 24
24.

Question 25
25.

Review Lesson 1-3: Simplify the algebraic expression.

Question 26
26.

Review Lesson 1-3: Simplify the algebraic expression.

Question 27
27.

Review Lesson 1-3: Simplify the algebraic expression.

Question 28
28.

Question 29
29.

Question 30
30.

Question 31
31.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Question 32
32.

Reflection: Math Success

Solve It! This equation contains an infinite radical.
Square each side. You get a quadratic equation that also contains an infinite radical.
Are the two solutions of the quadratic equation also solutions of this equation? Explain.
Hint: consider substitution from one equation into the other.
No. By substitution:
Therefore, the solutions of the quadratic equation are both positive and negative, as follows:
The solution to the original equation is positive.
Yes. Given that
and that radicals simplify to only real numbers that are positive, as shown here:
both equations must have the same solutions.
Problem 1 Got It? What are the fifth roots of 0, -1, and 32?
-32
-2
-1
no real root
0
1
2
32
Fifth root of 0
Fifth root of -1
Fifth root of 32
Problem 1 Got It? What are the real square roots of the following?
-0.1
-36/121
-6/11
no real root
0
0.1
6/11
36/121
Real square root(s) of
Real square root(s) of
Real square root(s) of
Problem 1 Got It? Reasoning: Explain why a negative real number b has no real nth roots if n is even.
Any negative number squared is a positive number. Therefore, there can be no real nth roots (where n is even) for a negative number b.
By the rational root theorem and since b can be written as the following polynomial:
it follows that the only rational roots of b will be the factors of b over the factors of 0, which equal 0.
By Descartes' Rule of Signs and since b can be written as the following polynomial with no sign changes:

it follows that there can be at most 0 real nth roots.
Question 5
5.

Question 6
6.

Question 7
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Question 8
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Question 9
9.

Question 10
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Question 11
11.

Question 12
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Question 13
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Question 14
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Question 15
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Question 16
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Question 17
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Question 18
18.

Review Lesson 5-9: Determine the cubic function that is obtained from the parent function y = x³ after the stated sequence of transformations.
translation up 3 units and left 2 units
vertical stretch by a factor of 3 and translation right 2 units
translation right 2 units and down 3 units
Review Lesson 4-7: Use the Quadratic Formula to identify the solution(s) of each quadratic equation.
Some solutions may not be used.
Solution(s) of:
Solution(s) of:
Solution(s) of:
Vocabulary Review: Identify the exponent(s) in each expression.
-3
0
2
4
5
7
12
21
Vocabulary Review: Which expression represents five to the second power ?
Use Your Vocabulary: Match each number in the left column to each term in the right column that best describes it as part of the equation.
4
81
√
3
radical
root
index
radicand
Problem 2 Got It?
A
B
C
D
Problem 2 Got It?
A
B
C
D
Problem 2 Got It?
A
B
C
D
Problem 2 Got It?
A
B
C
D
Problem 3 Got It?
A
B
C
D
Problem 3 Got It?
A
B
C
D
Problem 3 Got It?
A
B
C
D
Problem 4 Got It? Academics: Some teachers adjust test scores when a test is difficult. One teacher's formula for adjusting scores is show below, where A is the adjusted score and R is the raw score.
What are the adjusted scores for raw scores of 0 and 100?
A
B
C
D
What are all the real square roots of 25?
A
B
C
D
What are all the real square roots of 0.16?
A
B
C
D
What are all the real square roots of -64?
A
B
C
D
Simplify the radical expression.
A
B
C
D
Simplify the radical expression.
A
B
C
D
Simplify the radical expression.
A
B
C
D