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1.Why is Yasmine's work incorrect? Explain your reasoning below.    2. Simplify 2√(7+√8). Show your work

1.Why is Yasmine's work incorrect? Explain your reasoning below.    2. Simplify 2√(7+√8). Show your work

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1.Why is Yasmine's work incorrect? Explain your reasoning below. 

 

2. Simplify 2√(7+√8). Show your work?

**Problem: Simplify** Simplify \(\sqrt{2} \, (7 + \sqrt{8})\). Show your work. **Solution:** To simplify the expression \(\sqrt{2} \, (7 + \sqrt{8})\), we need to use the distributive property. 1. **Distribute \(\sqrt{2}\):** \(\sqrt{2} \times 7 + \sqrt{2} \times \sqrt{8}\) - For the first term: \(\sqrt{2} \times 7 = 7\sqrt{2}\) - For the second term: \(\sqrt{2} \times \sqrt{8} = \sqrt{16}\) 2. **Simplify \(\sqrt{16}\):** \(\sqrt{16} = 4\) 3. **Final Expression:** Combine the terms to get the simplified expression: \(7\sqrt{2} + 4\) **Conclusion:** The simplified form of the expression \(\sqrt{2} \, (7 + \sqrt{8})\) is \(7\sqrt{2} + 4\).
Transcribed Image Text:**Problem: Simplify** Simplify \(\sqrt{2} \, (7 + \sqrt{8})\). Show your work. **Solution:** To simplify the expression \(\sqrt{2} \, (7 + \sqrt{8})\), we need to use the distributive property. 1. **Distribute \(\sqrt{2}\):** \(\sqrt{2} \times 7 + \sqrt{2} \times \sqrt{8}\) - For the first term: \(\sqrt{2} \times 7 = 7\sqrt{2}\) - For the second term: \(\sqrt{2} \times \sqrt{8} = \sqrt{16}\) 2. **Simplify \(\sqrt{16}\):** \(\sqrt{16} = 4\) 3. **Final Expression:** Combine the terms to get the simplified expression: \(7\sqrt{2} + 4\) **Conclusion:** The simplified form of the expression \(\sqrt{2} \, (7 + \sqrt{8})\) is \(7\sqrt{2} + 4\).
**Yasmine's Work:** \[ \sqrt{56a^3b} \] \[ \sqrt{(2^3)(7)(a^3)(b)} \] \[ 2a\sqrt{7b} \] **Explanation:** Yasmine is simplifying the expression \(\sqrt{56a^3b}\). 1. **Prime Factorization:** She starts by breaking down 56 into its prime factors: \(2^3 \times 7\). 2. **Expression Breakdown:** She expresses \(56a^3b\) as \((2^3)(7)(a^3)(b)\) under the square root. 3. **Simplification:** Yasmine simplifies this to \(2a\sqrt{7b}\) by taking out perfect squares from under the square root.
Transcribed Image Text:**Yasmine's Work:** \[ \sqrt{56a^3b} \] \[ \sqrt{(2^3)(7)(a^3)(b)} \] \[ 2a\sqrt{7b} \] **Explanation:** Yasmine is simplifying the expression \(\sqrt{56a^3b}\). 1. **Prime Factorization:** She starts by breaking down 56 into its prime factors: \(2^3 \times 7\). 2. **Expression Breakdown:** She expresses \(56a^3b\) as \((2^3)(7)(a^3)(b)\) under the square root. 3. **Simplification:** Yasmine simplifies this to \(2a\sqrt{7b}\) by taking out perfect squares from under the square root.
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