Simplifying Radicals
Algebra 1, Unit 3, Day 1
Name: _________________________
Date: __________________________
Key Idea
To simplify a radical, find the largest perfect square (or perfect cube) that divides the number inside. Then, split the radical into two and simplify the "perfect" part.
\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)
Examples
\(\sqrt{50}\)
\( = \sqrt{25 \cdot 2} \)
\( = \sqrt{25} \cdot \sqrt{2} \)
\( = 5\sqrt{2} \)
\(\sqrt[3]{16}\)
\( = \sqrt[3]{8 \cdot 2} \)
\( = \sqrt[3]{8} \cdot \sqrt[3]{2} \)
\( = 2\sqrt[3]{2} \)
Practice Problems
Simplify each expression completely. Show your steps.
1. \(\sqrt{20}\)
2. \(\sqrt{48}\)
3. \(\sqrt{72}\)
4. \(\sqrt[3]{40}\)
5. \(\sqrt{180}\)
6. \(\sqrt{99}\)
7. \(5\sqrt{24}\)
8. \(2\sqrt[3]{108}\)
9. \(-2\sqrt[3]{54}\)
10. \(\sqrt{125}\)
11. \(3\sqrt{200}\)
12. \(\sqrt[3]{250}\)