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

Last updated over 4 years ago

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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.

A.SSE.2

G.CO.2

A.REI.4.b

A.SSE.2

100

A.SSE.2

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

Last updated over 4 years ago

32 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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.

A.SSE.2

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.

A.SSE.2

Problem 2 Got It?

A.SSE.2

Problem 2 Got It?

A.SSE.2

Problem 2 Got It?

A.SSE.2

Problem 2 Got It?

A.SSE.2

Problem 3 Got It?

A.SSE.2

Problem 3 Got It?

A.SSE.2

Problem 3 Got It?

A.SSE.2

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.SSE.2

What are all the real square roots of 25?

A.SSE.2

What are all the real square roots of 0.16?

A.SSE.2

What are all the real square roots of -64?

A.SSE.2

Simplify the radical expression.

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Simplify the radical expression.

A.SSE.2

Simplify the radical expression.

A.SSE.2

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

A.SSE.2

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

A.SSE.2

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

G.CO.2

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].

A.REI.4.b

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:

A.REI.4.b

Review Lesson 1-3: Simplify the algebraic expression.

A.SSE.2

Review Lesson 1-3: Simplify the algebraic expression.

A.SSE.2

Review Lesson 1-3: Simplify the algebraic expression.

A.SSE.2

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 ?

A.SSE.2

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.

radical
root
index
radicand

100

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.

Reflection: Math Success

A.SSE.2

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

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

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.

Problem 1 Got It? What are the fifth roots of 0, -1, and 32?

Problem 1 Got It? What are the real square roots of the following?

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

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

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?

What are all the real square roots of 25?

What are all the real square roots of 0.16?

What are all the real square roots of -64?

Simplify the radical expression.

Simplify the radical expression.

Simplify the radical expression.

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

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

Review Lesson 5-9: Determine the cubic function that is obtained from the parent function y = x³ after the stated sequence of transformations.

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].

Review Lesson 4-7: Use the Quadratic Formula to identify the solution(s) of each quadratic equation.Some solutions may not be used.

Review Lesson 1-3: Simplify the algebraic expression.

Review Lesson 1-3: Simplify the algebraic expression.

Review Lesson 1-3: Simplify the algebraic expression.

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

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.

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.

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.

Problem 1 Got It? What are the fifth roots of 0, -1, and 32?

Problem 1 Got It? What are the real square roots of the following?

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

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

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?

What are all the real square roots of 25?

What are all the real square roots of 0.16?

What are all the real square roots of -64?

Simplify the radical expression.

Simplify the radical expression.

Simplify the radical expression.

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

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

Review Lesson 5-9: Determine the cubic function that is obtained from the parent function y = x³ after the stated sequence of transformations.

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].

Review Lesson 4-7: Use the Quadratic Formula to identify the solution(s) of each quadratic equation.Some solutions may not be used.

Review Lesson 1-3: Simplify the algebraic expression.

Review Lesson 1-3: Simplify the algebraic expression.

Review Lesson 1-3: Simplify the algebraic expression.

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

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.

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.

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.

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?

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].

Review Lesson 4-7: Use the Quadratic Formula to identify the solution(s) of each quadratic equation.
Some solutions may not be used.

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.

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.

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?

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].

Review Lesson 4-7: Use the Quadratic Formula to identify the solution(s) of each quadratic equation.
Some solutions may not be used.

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.