Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter9: Roots And Radicals
Section9.4: Multiply Square Roots
Problem 313E: A garden will be made so as to contain two square sections, one section with side length 5+6 yards...
Related questions
Question
Simplify by performing the indicated operations:
Transcribed Image Text:The expression is \(2\sqrt{27} - 3\sqrt{75}\).
### Explanation:
1. **Simplification of Radicals:**
- \(\sqrt{27}\) can be simplified as \(\sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}\).
- \(\sqrt{75}\) can be simplified as \(\sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}\).
2. **Substitutions and Calculations:**
- Substituting the simplified radicals, the expression becomes:
- \(2(3\sqrt{3}) - 3(5\sqrt{3})\).
- Simplifying further:
- \(6\sqrt{3} - 15\sqrt{3} = -9\sqrt{3}\).
Thus, the simplified form of the expression is \(-9\sqrt{3}\).
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