Simplify the expression 18 16 Enter the exact, simplified answer.

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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**Simplifying Radical Expressions**

**Problem Statement:**
Simplify the expression 

\[
\sqrt{\frac{18}{16}}
\]

**Instructions:**
Enter the exact, simplified answer.

---

**Solution Steps:**

1. **Simplify the Fraction:**
   - The fraction \(\frac{18}{16}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
   - \(\frac{18}{16} = \frac{9}{8}\)

2. **Simplify the Radical Expression:**
   - The expression now becomes \(\sqrt{\frac{9}{8}}\).
   - This can be rewritten as \(\frac{\sqrt{9}}{\sqrt{8}}\).

3. **Compute the Square Roots:**
   - \(\sqrt{9} = 3\)
   - \(\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}\)

4. **Combine and Simplify:**
   - \(\frac{3}{2\sqrt{2}}\)

5. **Rationalize the Denominator:**
   - To rationalize, multiply the numerator and the denominator by \(\sqrt{2}\):
   - \(\frac{3\sqrt{2}}{2\sqrt{2} \times \sqrt{2}} = \frac{3\sqrt{2}}{2 \times 2}\)
   - \(\frac{3\sqrt{2}}{4}\)

**Final Answer:** \(\frac{3\sqrt{2}}{4}\)

This simplified expression is the exact answer for the given problem.
Transcribed Image Text:**Simplifying Radical Expressions** **Problem Statement:** Simplify the expression \[ \sqrt{\frac{18}{16}} \] **Instructions:** Enter the exact, simplified answer. --- **Solution Steps:** 1. **Simplify the Fraction:** - The fraction \(\frac{18}{16}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. - \(\frac{18}{16} = \frac{9}{8}\) 2. **Simplify the Radical Expression:** - The expression now becomes \(\sqrt{\frac{9}{8}}\). - This can be rewritten as \(\frac{\sqrt{9}}{\sqrt{8}}\). 3. **Compute the Square Roots:** - \(\sqrt{9} = 3\) - \(\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}\) 4. **Combine and Simplify:** - \(\frac{3}{2\sqrt{2}}\) 5. **Rationalize the Denominator:** - To rationalize, multiply the numerator and the denominator by \(\sqrt{2}\): - \(\frac{3\sqrt{2}}{2\sqrt{2} \times \sqrt{2}} = \frac{3\sqrt{2}}{2 \times 2}\) - \(\frac{3\sqrt{2}}{4}\) **Final Answer:** \(\frac{3\sqrt{2}}{4}\) This simplified expression is the exact answer for the given problem.
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