Rationalizing the Denominator
Name: _________________________
Date: __________________________
Worked-Out Examples
Example 1: Basic
\( \frac{2}{\sqrt{5}} \)
\(\rightarrow \frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}\)
\(\rightarrow \frac{2\sqrt{5}}{5}\)
Example 2: Simplify First
\( \frac{5}{\sqrt{12}} \)
\(\rightarrow \frac{5}{\sqrt{4 \cdot 3}} = \frac{5}{2\sqrt{3}}\)
\(\rightarrow \frac{5}{2\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{2 \cdot 3}\)
\(\rightarrow \frac{5\sqrt{3}}{6}\)
Practice Problems
Simplify each expression by rationalizing the denominator.
1. \( \frac{1}{\sqrt{7}} \)
2. \( \frac{6}{\sqrt{3}} \)
3. \( \frac{15}{\sqrt{5}} \)
4. \( \sqrt{\frac{2}{3}} \)
5. \( \frac{1}{\sqrt{8}} \)
6. \( \frac{12}{\sqrt{18}} \)
7. \( \frac{5}{\sqrt{50}} \)
8. \( \frac{\sqrt{3}}{\sqrt{6}} \)
9. \( \frac{4}{3\sqrt{2}} \)
10. \( \sqrt{\frac{7}{12}} \)
11. \( \frac{3\sqrt{5}}{\sqrt{2}} \)
12. \( \frac{2\sqrt{5}}{\sqrt{80}} \)