OML Search

Existence and Uniqueness of Square and Cube Roots





 


Videos to help Grade 8 students learn that the positive square root and cube root exists for all positive numbers and is unique and solve simple equations that require them to find the square or cube root of a number.

New York State Common Core Math Grade 8, Module 7, Lesson 3

Related Topics:
Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Lesson 3 Student Outcomes

• Students know that the positive square root and cube root exists for all positive numbers and is unique.
• Students solve simple equations that require them to find the square or cube root of a number.

Lesson 3 Summary

The square or cube root of a positive number exists, and there can be only one positive square root or one cube root of the number.

Lesson 3 Classwork

Opening
Find the Rule Part 1
Find the Rule Part 2
Exercises 1–9
Find the positive value of that makes each equation true. Check your solution.
1. x2 = 169
a. Explain the first step in solving this equation.
b. Solve the equation and check your answer.

2. A square-shaped park has an area of 324 ft2. What are the dimensions of the park? Write and solve an equation.
3. 625 = x2
4. A cube has a volume of 27 in3. What is the measure of one of its sides? Write and solve an equation.
5. What positive value of makes the following equation true: x2 = 64? Explain.
6. What positive value of makes the following equation true: x3 = 64? Explain.
7. x2 = 256-1 Find the positive value of x that makes the equation true.
8. x3 = 343-1 Find the positive value of x that makes the equation true.
9. Is 6 a solution to the equation x2 - 4 = 5x? Explain why or why not.




Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.



OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines