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

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by Matthew Richardson

| 32 QuestionsNote from the author:

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.

1

10 pts

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.

2

10 pts

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

3

10 pts

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

4

10 pts

Problem 1 Got It? Reasoning: Explain why a negative real number b has no real nth roots if n is even.

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.

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.

5

5

10 pts

Problem 2 Got It?

A

B

C

D

6

6

10 pts

Problem 2 Got It?

A

B

C

D

7

7

10 pts

Problem 2 Got It?

A

B

C

D

8

8

10 pts

Problem 2 Got It?

A

B

C

D

9

9

10 pts

Problem 3 Got It?

A

B

C

D

10

10

10 pts

Problem 3 Got It?

A

B

C

D

11

11

10 pts

Problem 3 Got It?

A

B

C

D

12

12

10 pts

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

13

13

10 pts

What are all the real square roots of 25?

A

B

C

D

14

14

10 pts

What are all the real square roots of 0.16?

A

B

C

D

15

15

10 pts

What are all the real square roots of -64?

A

B

C

D

16

16

10 pts

Simplify the radical expression.

A

B

C

D

17

17

10 pts

Simplify the radical expression.

A

B

C

D

18

18

10 pts

Simplify the radical expression.

A

B

C

D

19

10 pts

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

21

10 pts

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

22

10 pts

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

23

10 pts

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].

24

10 pts

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:

25

10 pts

Review Lesson 1-3: Simplify the algebraic expression.

26

10 pts

Review Lesson 1-3: Simplify the algebraic expression.

27

10 pts

Review Lesson 1-3: Simplify the algebraic expression.

28

10 pts

Vocabulary Review: Identify the exponent(s) in each expression.

- -3
- 0
- 2
- 4
- 5
- 7
- 12
- 21

29

10 pts

Vocabulary Review: Which expression represents five to the second power ?

30

10 pts

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

31

100 pts

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.

32

10 pts

Reflection: Math Success

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