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MA.8.AR.2.3 · Algebraic Reasoning

Solving Equations with Square Roots and Cube Roots: Sample FAST Questions

Equations of the form x^2 = p and x^3 = q are the 8th grade introduction to solving with roots. A squared equation has two real solutions, one positive and one negative, while a cubed equation has exactly one, and that one can be negative.

How the FAST tests this benchmark

FAST items include equation editor answers, multiselect items where students choose every solution, and multiple choice items that quietly offer only the positive root. Perfect squares stay at or below 225 and perfect cubes run from −125 to 125.

Skills students need

  • Solve x^2 = p and report both solutions
  • Solve x^3 = q, including negative values of q
  • Recall perfect squares up to 225 and perfect cubes from −125 to 125
  • Check a solution by substituting it back

Try 6 real MA.8.AR.2.3 questions

These come straight from Algebro's 8th grade pre-algebra question bank, easiest first. Answer one, check it, then move to the next.

Question 1 of 6

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Question 1EasyDrop-Down
Solve x2=196x^2 = 196. Choose the value of 196\sqrt{196} to complete the solution x=±x = \pm .

Showcase extra: the real practice and quiz players do not have this button.

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More 8th grade algebraic reasoning benchmarks

MA.8.AR.4.1

Checking Solutions to Systems of Equations

MA.8.AR.4.2

How Many Solutions a Graphed System Has

MA.8.AR.4.3

Solving Systems of Equations by Graphing

MA.8.AR.2.3: Square and Cube Roots Practice | Algebro