Grade 10: Square and Cube Root Equations
This worksheet focuses on solving square and cube root equations, including identifying extraneous solutions, for Grade 10 math students.
Includes
Standards
Topics
Square and Cube Root Equations
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Read each question carefully and solve for the variable. Remember to check for extraneous solutions.
Match the equation type with its defining characteristic.
1. Square Root Equation
a. Involves a variable under a cube root symbol.
2. Cube Root Equation
b. Involves a variable under a square root symbol.
Solve the following square root equations. Be sure to check for extraneous solutions.
1. √(x + 3) = 4
2. √(2x - 1) + 5 = 8
Solve the following cube root equations.
1. ³√(x - 5) = 2
2. ³√(3x + 1) - 4 = -1
Indicate whether each statement is True or False.
1. An extraneous solution is a solution that satisfies the original equation.
True
False
2. When solving a square root equation, you must always square both sides.
True
False
Complete the following sentences.
1. To eliminate a square root, you must both sides of the equation.
2. An solution is a value that is obtained through algebraic manipulation but does not satisfy the original equation.
1. Which of the following is an extraneous solution for the equation √(x) = -2?
x = 4
x = 2
x = -4
No extraneous solution
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