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qid 8602 · math
Question: Simplify the fraction by rationalizing the denominator: $$\frac{4}{\sqrt{108}+2\sqrt{12}+2\sqrt{27}}.$$
- \frac{1}{4\sqrt{27}}
- \frac{1}{2\sqrt{3}}
- 2\sqrt{12}
- \frac{1}{4\sqrt{3}}
- 2\sqrt{27}
- \frac{4\sqrt{3}}{33}
- \frac{4\sqrt{3}}{27}
- \frac{4\sqrt{3}}{12}
- \frac{4\sqrt{3}}{108}
- \frac{\sqrt{3}}{12}
Our answer: J. \frac{\sqrt{3}}{12} Source quote machine-checked (exact quote)
How it was answered
Multi-step solver (maze), replayed by code
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)
Earlier version (superseded)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)
Earlier version (superseded)
No public source has been found for this card yet (3 places checked internally).
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