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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn how to use factors of a number to simplify a square root.

### New York State Common Core Math Grade 8, Module 7, Lesson 5

^{2} = p and x^{3} = p

^{2} = p
or x^{3} = p where p is a positive rational number, then take the
square or cube root to determine the positive value of x.

Lesson 5 Classwork

Example 1

Solve the non-linear equation:

x^{3} + 9x = 1/2(18x + 54)

Example 2

Solve the non-linear equation:

x(x - 3) - 51 = -3x + 13

Exercises 1–8

Find the positive value of that makes each equation true, and then verify your solution is correct.

1. Solve x^{2} - 14 = 5x + 67 - 5x

Explain how you solved the equation.

2. Solve and simplify: x(x - 1) = 121 - x

3. A square has a side length of 3x and an area of 324 in^{2}. What is the value of x?

7. What are we trying to determine in the diagram below?

Determine the value of and check your answer.

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.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn how to use factors of a number to simplify a square root.

Download Worksheets for Grade 8, Module 7, Lesson 5

Lesson 5 Student Outcomes

• Students find the positive solutions for equations of the form xLesson 5 Summary

Equations that contain variables that are squared or cubed can be solved using the properties of equality and the definition of square and cube roots. Simplify an equation until it is in the form of xLesson 5 Classwork

Example 1

Solve the non-linear equation:

x

Example 2

Solve the non-linear equation:

x(x - 3) - 51 = -3x + 13

Exercises 1–8

Find the positive value of that makes each equation true, and then verify your solution is correct.

1. Solve x

Explain how you solved the equation.

2. Solve and simplify: x(x - 1) = 121 - x

3. A square has a side length of 3x and an area of 324 in

7. What are we trying to determine in the diagram below?

Determine the value of and check your answer.

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.

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