We will learn how to multiply and divide expressions containing radicals.
Formulas for Multiplication and Division
√a × √b = √(a×b)（a ≥ 0, b ≥ 0）
√a ÷ √b = √(a÷b)（a ≥ 0, b > 0）
📘 Example ①
Calculate √3 × √5.
Solution: √3 × √5 = √(3×5) = √15
Calculate √3 × √5.
Solution: √3 × √5 = √(3×5) = √15
📘 Example ②
Calculate √18 ÷ √2.
Solution: √18 ÷ √2 = √(18÷2) = √9 = 3
Calculate √18 ÷ √2.
Solution: √18 ÷ √2 = √(18÷2) = √9 = 3
💡 Key Points
- Simplify the expression inside the radical (√12 = √(4×3) = 2√3)
- The result of a calculation may be an integer
- Calculate the coefficient and radical part separately (2√3 × 3√5 = 6√15)
Practice Problems
- Calculate √2 × √7.
- Calculate √24 ÷ √6.
Answers and Explanations
- Answer: √2 × √7 = √14
- Answer: √24 ÷ √6 = √(24÷6) = √4 = 2