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.
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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