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2/27 – 3/75

2/27 – 3/75

Intermediate Algebra
Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter8: Roots And Radicals
Section8.4: Add, Subtract, And Multiply Radical Expressions
Problem 241E: Explain the when a radical expression is in simplest form.
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Question

Simplify by performing the indicated operations: 

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 \(-9\sqrt{3}\).
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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