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Radical Functions and Rational Exponents — High School Algebra 2 practice questions

16 multiple-choice questions and 12 flashcards on Radical Functions and Rational Exponents, about 11% of the High School Algebra 2 bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-12 · how we write and review questions

What this chapter covers

Radical Functions and Rational Exponents is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 16 of the bank's 150 multiple-choice questions — roughly 11% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Radical Functions and Rational Exponents practice questions

2 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

Evaluate 16^(3/4).

  1. 12
  2. 64
  3. 8
  4. 4096

Answer: C — 8

C) Correct — Take the fourth root first: 16^(1/4) = 2, then 2³. A) Multiplies 16 by 3/4. B) Computes 4³ instead. D) Cubes 16 before taking the root, then stops.

What is the domain of f(x) = √(9 − x²)?

  1. −3 ≤ x ≤ 3
  2. x ≥ 3 or x ≤ −3
  3. −3 < x < 3
  4. x ≤ 3

Answer: A — −3 ≤ x ≤ 3

A) Correct — Need 9 − x² ≥ 0. B) Reverses the inequality. C) Excludes the endpoints. D) Forgets the lower bound.

Radical Functions and Rational Exponents flashcards

3 cards from the 12 in this chapter.

Simplify √50.

5√2. (√(25 × 2) = 5√2.)

What's x^(2/3)?

∛(x²) = (∛x)².

What's 8^(2/3)?

4. (∛8)² = 2² = 4.

Practise the full chapter

These are a sample. The full Radical Functions and Rational Exponents chapter runs 28 items with per-chapter progress tracking, on the web and in the iOS app.

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