Unit 2: Operations on Radicals (Math 20-1)
Entire/mixed radicals; add/subtract like radicals; multiply/divide radicals; simplification and rationalizing denominators.
Entire ⇄ Mixed
Simplify \( \sqrt[n]{a} \)
Combine like radicals
Multiply/Divide \( \sqrt[n]{a}\,\sqrt[n]{b} \)
Rationalize denominators
What You Should Be Able To Do
- Convert between entire and mixed radicals for integer indices \(n\ge2\).
- Simplify radicals by extracting perfect \(n\)th powers.
- Add/subtract radicals by first simplifying and then combining like radicals (same index and radicand).
- Multiply/divide radicals with the same index and simplify; rationalize monomial radical denominators.
- Communicate restrictions (e.g., even index with non-negative radicand in real numbers).
Progress autosaves to this device.
Video Library
Entire & Mixed Radicals
Move factors in/out of the radical for index \(n\).
youtube.com – “entire and mixed radicals”Simplifying Radicals
Prime powers, extracting perfect \(n\)th powers.
youtube.com – “simplifying radicals prime factorization”Adding/Subtracting Radicals
Like radicals only after simplifying.
youtube.com – “adding and subtracting radicals”Multiply/Divide & Rationalize
Same index rule, monomial rationalization.
youtube.com – “multiplying dividing radicals rationalizing denominators”Interactive Tools
Entire ⇄ Mixed Radical Converter
Radical Simplifier
| Prime | Exponent | Groups of \(n\) | Remainder |
|---|
Add/Subtract Like Radicals
Same index and same simplified radicand are required to combine.
Multiply/Divide Radicals (Monomial)
Unit 2 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: \(\sqrt{200}\), \(3\sqrt{8}+2\sqrt{18}-\sqrt{50}\), \(\sqrt[3]{24}\cdot 2\sqrt[3]{6}\), \(\dfrac{5}{\sqrt[3]{2}}\).