Operations with Radicals
Name: _________________________
Date: __________________________
Worked-Out Examples
Example 1: Simplify then Add
\( \sqrt{12} + \sqrt{75} \)
\(\rightarrow \sqrt{4 \cdot 3} + \sqrt{25 \cdot 3}\)
\(\rightarrow 2\sqrt{3} + 5\sqrt{3}\)
\(\rightarrow 7\sqrt{3}\)
Example 2: Multiply then Simplify
\( 2\sqrt{5} \cdot 3\sqrt{10} \)
\(\rightarrow (2 \cdot 3)\sqrt{5 \cdot 10}\)
\(\rightarrow 6\sqrt{50}\)
\(\rightarrow 6\sqrt{25 \cdot 2} \rightarrow 6 \cdot 5\sqrt{2}\)
\(\rightarrow 30\sqrt{2}\)
Practice Problems
Simplify each expression completely. Show your work.
1. \( 7\sqrt{6} + 2\sqrt{6} \)
2. \( 12\sqrt{11} - 8\sqrt{11} \)
3. \( \sqrt{10} \cdot \sqrt{5} \)
4. \( \sqrt{27} + \sqrt{48} \)
5. \( \sqrt{125} - \sqrt{20} \)
6. \( 3\sqrt{6} \cdot 4\sqrt{2} \)
7. \( 3\sqrt{8} + 5\sqrt{2} \)
8. \( \sqrt{72} - \sqrt{50} \)
9. \( -4\sqrt{3} \cdot \sqrt{3} \)
10. \( \sqrt{5}(\sqrt{10} + 3) \)
11. \( 2\sqrt{12} + 5\sqrt{300} \)
12. \( 3\sqrt{50} - \sqrt{32} \)