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qid 8602 · math

Question: Simplify the fraction by rationalizing the denominator: $$\frac{4}{\sqrt{108}+2\sqrt{12}+2\sqrt{27}}.$$

  1. \frac{1}{4\sqrt{27}}
  2. \frac{1}{2\sqrt{3}}
  3. 2\sqrt{12}
  4. \frac{1}{4\sqrt{3}}
  5. 2\sqrt{27}
  6. \frac{4\sqrt{3}}{33}
  7. \frac{4\sqrt{3}}{27}
  8. \frac{4\sqrt{3}}{12}
  9. \frac{4\sqrt{3}}{108}
  10. \frac{\sqrt{3}}{12}

Our answer: J. \frac{\sqrt{3}}{12} Source quote machine-checked (exact quote)

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How it was answered

Multi-step solver (maze), replayed by code

card: maze · card sha256 39464f7b4168f513…

Current source

OpenStax Intermediate Algebra 2e, Section 8.5 Divide Radical Expressions

https://openstax.org/books/intermediate-algebra-2e/pages/8-5-divide-radical-expressions

“To rationalize a denominator with one term, we can multiply a square root by itself. To keep the fraction equivalent, we multiply both the numerator and denominator by the same factor.”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T01:08:25.301Z

page text sha256 d5d1bdd54e15eee9… · content sha256 5de05e0db31abd5c…

addendum maze_qid8602_b4_maze_input_ADDENDUM_source_rs20260918T010825Z · sha256 8756dd6910ff184e… · replaces the version below, addendum sha256 52e6ef2807329fde…

Earlier version (superseded)

https://openstax.org/books/intermediate-algebra-2e/pages/8-5-divide-radical-expressions

Source weak (http_get_200_text_and_question_terms)

retrieved 2026-09-17T23:24:49.304Z

page text sha256 713aad0eb106ce02… · content sha256

addendum maze_qid8602_b4_maze_input_ADDENDUM_source_bf20260917T232449Z · sha256 52e6ef2807329fde… · replaces the version below, addendum sha256 b353986a2d00d622…

Earlier version (superseded)

No public source has been found for this card yet (3 places checked internally).

addendum maze_qid8602_b4_maze_input_ADDENDUM_source · sha256 b353986a2d00d622…

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