JAMB 2015 Mathematics · Question 6
Simplify ×
Options
- A.10 √3
- B.5 √3
- C.20 √3
- D.15 √3
Answer: C. 20 √3
Explanation written with AI and checked against the answer key
Analyze the question: We need to multiply two square roots and simplify the result into the form a√b. Concept: For non-negative numbers, √a × √b = √(a × b). To simplify, pull out any perfect-square factors from under the root. Solution: √30 × √40 = √(30 × 40) = √1200 Now factorise 1200 using a perfect square: 1200 = 400 × 3 √1200 = √400 × √3 = 20√3 Checking the answer: √30 ≈ 5.477 and √40 ≈ 6.325, so the product ≈ 34.64. Also 20√3 ≈ 20 × 1.732 = 34.64. ✓ Answer: Option C, 20√3. Tip: Look for the biggest perfect square factor (4, 9, 16, 25, 100, 400...). Here, spotting that 30 × 40 = 12 × 100 = 1200 and 1200 = 400 × 3 saves time. Another shortcut: √30 × √40 = √3 × √10 × √4 × √10 = (√10 × √10) × 2 × √3 = 10 × 2 × √3 = 20√3. Pulling out the √10 pairs makes it quick. You can also quickly rule out options by estimating: the answer must be about 34.6, and only 20√3 gives that.AI can make mistakes. Report anything that looks wrong.
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