Solving Radical Equations

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

Worksheets for Grade 8

Lesson 5 Student Outcomes

• Students find the positive solutions for equations of the form x² = p and x³ = p

Lesson 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 x² = p or x³ = 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:
x³ + 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 x² - 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 in². 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.

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