Free Printable WorksheetMathGrade 8Math Curriculum8.EE.A.2

8.8 Understanding Positive and Negative Square Roots Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.8 Understanding Positive and Negative Square Roots. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.8 Understanding Positive and Negative Square Roots - Which option correctly identifies the value of sqrt(a) and the complete solution set to x^2 = a? (CCSS 8.EE.A.2; CA 8.EE.A.2; MA 8.EE.A.2)

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

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related 8.8 Understanding Positive and Negative Square Roots skill assessments:

Problem 1Difficulty: Hard
For a nonnegative number a, which statement best summarizes when x2 = a has one real solution and when it has two?
AIt has one real solution when a = 0 and two opposite real solutions when a > 0
BIt always has two real solutions for every nonnegative a
CIt always has one real solution because sqrt(a) is one number
DIt has one real solution when a > 0 and two when a = 0
Solution & Explanation:When a = 0, the only solution is x = 0. When a is positive, the equation x2 = a has the two opposite real solutions -sqrt(a) and sqrt(a).
Problem 2Difficulty: Hard
Choose the only correct chain of statements.
Asqrt(225) = 15; -sqrt(225) = -15; x2 = 225 has solutions -15 and 15
Bsqrt(225) = -15; -sqrt(225) = 15; x2 = 225 has solution 15 only
Csqrt(225) = {-15, 15}; -sqrt(225) = {-15, 15}; x2 = 225 has one solution
Dsqrt(225) = 15; -sqrt(225) = 15; x2 = 225 has solutions -225 and 225
Solution & Explanation:The principal square root of 225 is 15, so its opposite is -15. The equation x2 = 225 is solved by both -15 and 15.
Problem 3Difficulty: Hard
Which set of directions would correctly fix the statement sqrt(0.49) = -0.7 or 0.7?
AReplace it with sqrt(0.49) = 0.7 and note that x2 = 0.49 has solutions -0.7 and 0.7
BReplace it with sqrt(0.49) = -0.7 because the square root should be negative
CKeep it the same because both numbers square to 0.49
DReplace it with sqrt(0.49) = {-0.7, 0.7}
Solution & Explanation:The radical expression should equal the principal root 0.7. The pair -0.7 and 0.7 belongs to the solution set of x2 = 0.49, not to sqrt(0.49).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.EE.A.2 (Primary standard selected for prompt fields: CCSS 8.EE.A.2. Skill statement: Which option correctly identifies the value of sqrt(a) and the complete solution set to x^2 = a? Associated standards listed with this skill: CCSS 8.EE.A.2; CA 8.EE.A.2; MA 8.EE.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).

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