Enter the values for the variables that give the correct simplified expressions, x = 2 0. V50x2 = /25-2-x² =5xyb %3D b = V32x = 16-2-x = ev2x %3D c = 18n 9-2-n= ev2n %3D e = V72x2 = V36 2- x2 = gxv2

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter0: A Review Of Basic Algebra
Section0.4: Polynomials
Problem 130E
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**Simplification of Square Root Expressions**

**Objective:**
Enter the values for the variables that give the correct simplified expressions, \( x \ge 0 \).

1. \(\sqrt{50x^2} = \sqrt{25 \cdot 2 \cdot x^2} = 5x\sqrt{b}\)
   - **b =** \(\_\_\_\_\_ \)
   
2. \(\sqrt{32x} = \sqrt{16 \cdot 2 \cdot x} = c\sqrt{2x}\)
   - **c =** \(\_\_\_\_\_ \)
   
3. \(\sqrt{18n} = \sqrt{9 \cdot 2 \cdot n} = e\sqrt{2n}\)
   - **e =** \(\_\_\_\_\_ \)

4. \(\sqrt{72x^2} = \sqrt{36 \cdot 2 \cdot x^2} = gx\sqrt{2}\)
   - **g =** \(\_\_\_\_\_ \)

**Instructions:**
Enter the correct values for \( b, c, e, \) and \( g \) to complete the simplified expressions.

**Solutions:**
- **b**: For the expression \(\sqrt{50x^2}\), we identify \(b\) such that \(5x\sqrt{b}\). Here, \(b = 2\).
- **c**: For the expression \(\sqrt{32x}\), we identify \(c\) such that \(c\sqrt{2x}\). Here, \(c = 4\).
- **e**: For the expression \(\sqrt{18n}\), we identify \(e\) such that \(e\sqrt{2n}\). Here, \(e = 3\).
- **g**: For the expression \(\sqrt{72x^2}\), we identify \(g\) such that \(gx\sqrt{2}\). Here, \(g = 6\).

**Review:** Ensure each value correctly simplifies the expression within the given constraints. If you encounter any issues, revisit the steps and re-evaluate your calculations.
Transcribed Image Text:**Simplification of Square Root Expressions** **Objective:** Enter the values for the variables that give the correct simplified expressions, \( x \ge 0 \). 1. \(\sqrt{50x^2} = \sqrt{25 \cdot 2 \cdot x^2} = 5x\sqrt{b}\) - **b =** \(\_\_\_\_\_ \) 2. \(\sqrt{32x} = \sqrt{16 \cdot 2 \cdot x} = c\sqrt{2x}\) - **c =** \(\_\_\_\_\_ \) 3. \(\sqrt{18n} = \sqrt{9 \cdot 2 \cdot n} = e\sqrt{2n}\) - **e =** \(\_\_\_\_\_ \) 4. \(\sqrt{72x^2} = \sqrt{36 \cdot 2 \cdot x^2} = gx\sqrt{2}\) - **g =** \(\_\_\_\_\_ \) **Instructions:** Enter the correct values for \( b, c, e, \) and \( g \) to complete the simplified expressions. **Solutions:** - **b**: For the expression \(\sqrt{50x^2}\), we identify \(b\) such that \(5x\sqrt{b}\). Here, \(b = 2\). - **c**: For the expression \(\sqrt{32x}\), we identify \(c\) such that \(c\sqrt{2x}\). Here, \(c = 4\). - **e**: For the expression \(\sqrt{18n}\), we identify \(e\) such that \(e\sqrt{2n}\). Here, \(e = 3\). - **g**: For the expression \(\sqrt{72x^2}\), we identify \(g\) such that \(gx\sqrt{2}\). Here, \(g = 6\). **Review:** Ensure each value correctly simplifies the expression within the given constraints. If you encounter any issues, revisit the steps and re-evaluate your calculations.
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