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

Last updated about 4 years ago

32 questions

Note 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.

100

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?

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

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?

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.

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.

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?