Activity 2: Simply Me!
Directions: Simplify each radical expression using any of the appropriate the laws of radicals.
Answer:
1) √90x²y³ → 3√10xy√y
2) √100x⁵y⁶ → 10x⁵y⁶
3) ⁴√243a⁶b⁸c⁹ → 3⁴√3a⁶b⁸c⁹
Solution:
1) √90x²y³
→ √90x²y³ = 90√x² √y³
→ √90x√y³
→ Simplify √³ = y√y
→ √90xy√y
→ √90=3√10
→ 3√10xy√y
2) √100x⁵y⁶
→ √100x⁵y⁶ = √10x²x⁵y⁶
→ √10x⁵y⁶
3) √243a⁶b⁸c⁹
→ √243a⁶b⁸c⁹ = 3 ⁴√3⁵ a⁶b⁸c⁹ (Prime factorization of 243=3⁵)
→ 3⁵=4⁴· 3 =⁴√3⁴· 3 a⁶b⁸c⁹
→ ⁴√3⁴ · 3 =⁴√3⁴ ⁴√3
→ ⁴√3⁴ ⁴√3a⁶b⁸c⁹
→ ⁴√3⁴ = 3
→ 3⁴√3a⁶b⁸c⁹
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