Free Printable WorksheetMathAlgebra IMath CurriculumALG1.103

ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.103 Solve Radical Equations and Check Solutions (Optional) - Select the correct solution to simple radical equations and check for extraneous solutions; Select the explanation that correctly explains why squaring both sides can introduce solutions that do not work.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key skill assessments:

Problem 1Difficulty: Mastery

Which final solution set and explanation are correct for sqrt(20x + 9) = 2x + 3?

Ax = 0 only because x = 2 is extraneous

Bx = 2 only because x = 0 makes the right side negative

Cx = 0 and x = 2 because both check in the original equation

DNo solution because squaring creates only extraneous values

Solution & Explanation:The squared equation gives x = 0 and x = 2. Checking gives sqrt(9) = 3 and 2(0) + 3 = 3, and sqrt(49) = 7 and 2(2) + 3 = 7.

Problem 2Difficulty: Mastery

A student squares sqrt(x - 3) = x - 5 and gets x = 4 and x = 7. Which sentence correctly explains x = 4?

AIt is a solution because sqrt(1) = 1

BIt is extraneous because sqrt(1) = 1 but 4 - 5 = -1

CIt is impossible because the radicand is negative

DIt should be kept because 4 is less than 7

Solution & Explanation:The original equation must be checked. At x = 4, the left side is 1 but the right side is -1, so x = 4 is extraneous.

Problem 3Difficulty: Mastery

Which check confirms that x = 10 solves sqrt(4x + 24) = x - 2?

Asqrt(64) = 8 and 10 - 2 = 8

Bsqrt(40) = 10 and 10 - 2 = 8

Csqrt(4x + 24) = 64 and x - 2 = 8

Dsqrt(10) = 4 and 10 - 2 = 8

Solution & Explanation:Substitute x = 10 into the original equation. The left side is sqrt(64) = 8 and the right side is 8.

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Frequently Asked Questions

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QHow do I download and print this ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key worksheet?

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QIs this ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key worksheet free for teachers and homeschoolers?

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QCan students practice ALG1.103 Solve Radical Equations and Check Solutions (Optional) Answer Key online with instant feedback?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard ALG1.103 (Students solve radical equations, check candidate solutions in the original equation, and explain why squaring both sides can introduce extraneous solutions.).